| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
01 Apr 2007 12:59:13 AM |
| Object: |
Supersymmetry Question |
I am under the impression that under Supersymmetry, transforming a
particle to its superpartner and back (electron->selectron->electron)
leaves the particle unchanged but displaced physically. Is this still
considered correct, or not? If so, is this displacement visible in
ordinary spacetime, or in one or more of the "extra" dimensions
presumed required for Supersymmetry?
I realize that some other group like sci.physics.strings migh be
more appropriate but I'm not looking for a deep mathematical
explanation; I'm getting plenty of those from Google which simply are
not clear as to whether they mean what dimensions I can see, or those
I can't.
Any help appreciated.
Mark L. Fergerson
.
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| User: "" |
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| Title: Re: Supersymmetry Question |
01 Apr 2007 05:39:05 PM |
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On 1 Apr, 06:59, "n...@bid.ness" <Alien8...@gmail.com> wrote:
I am under the impression that under Supersymmetry, transforming a
particle to its superpartner and back (electron->selectron->electron)
leaves the particle unchanged but displaced physically. Is this still
considered correct, or not? If so, is this displacement visible in
ordinary spacetime, or in one or more of the "extra" dimensions
presumed required for Supersymmetry?
Well the first thing I should say is that extra dimensions are *not*
required for supersymmetry; indeed most introductory courses teach
supersymmetry in 3+1 dimensions (this turns out to be a relatively
easy case due to the nice relationship between the Lorentz group and
its double cover, as well as being physically relevant). SuperSTRING
theory requires extra dimensions for reasons I couldn't claim to
understand, but one can perfectly well consider ordinary field
theories which are supersymmetric.
As for the rest of your question, I'm not sure that it makes sense. I
think that you may be confusing supersymmetry transformations (which
are a group of symmetries of a theory) with the generators Q and Qbar
of those transformations. Q or Qbar acts on a bosonic state to give a
fermionic state and vice-versa, but a supersymmetry transformation
acting on an electron will leave the system in a mixed state with both
electron and selectron. Since the transformations form a group, any
two supersymmetry transformations performed one after the other are
the same as a single supersymmetry transformation, so talking about a
supersymmetry transformation followed by another is redundant. In
particular to any transformation there is an inverse, so one can
transform an electron into a mixed state and back again without
changing a thing.
If we act on an electron twice with generators epsilon*Q +
epsilonbar*Qbar I think that we get back some linear combination of
the momenta operators acting on the electron; since momentum is the
generator of translations, perhaps this is what you have in mind?
If I find the time I will think about this question in the hope of
coming up with a more satisfactory answer.
-Rotwang
.
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| User: "" |
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| Title: Re: Supersymmetry Question |
02 Apr 2007 01:47:30 AM |
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On Apr 1, 3:39 pm, wrote:
On 1 Apr, 06:59, "n...@bid.ness" <Alien8...@gmail.com> wrote:
I am under the impression that under Supersymmetry, transforming a
particle to its superpartner and back (electron->selectron->electron)
leaves the particle unchanged but displaced physically. Is this still
considered correct, or not? If so, is this displacement visible in
ordinary spacetime, or in one or more of the "extra" dimensions
presumed required for Supersymmetry?
Well the first thing I should say is that extra dimensions are *not*
required for supersymmetry; indeed most introductory courses teach
supersymmetry in 3+1 dimensions (this turns out to be a relatively
easy case due to the nice relationship between the Lorentz group and
its double cover, as well as being physically relevant). SuperSTRING
theory requires extra dimensions for reasons I couldn't claim to
understand, but one can perfectly well consider ordinary field
theories which are supersymmetric.
I've been Googling SuSy for a couple days and indeed get the
impression that it is currently (considering it's been blended into
superstring theory) thought to require more than 3+1 spacetime
dimensions, though I could easily have that wrong.
As for the rest of your question, I'm not sure that it makes sense. I
think that you may be confusing supersymmetry transformations (which
are a group of symmetries of a theory) with the generators Q and Qbar
of those transformations. Q or Qbar acts on a bosonic state to give a
fermionic state and vice-versa, but a supersymmetry transformation
acting on an electron will leave the system in a mixed state with both
electron and selectron. Since the transformations form a group, any
two supersymmetry transformations performed one after the other are
the same as a single supersymmetry transformation, so talking about a
supersymmetry transformation followed by another is redundant. In
particular to any transformation there is an inverse, so one can
transform an electron into a mixed state and back again without
changing a thing.
The mixed state thing I have not yet run across and is entirely "who
ordered that!?" undesired. Oh, well.
Also yes, in the event of a transformation and its inverse being
applied sequentially nothing changes except the location of the
particle, at least that's what I think I'm reading.
If we act on an electron twice with generators epsilon*Q +
epsilonbar*Qbar I think that we get back some linear combination of
the momenta operators acting on the electron; since momentum is the
generator of translations, perhaps this is what you have in mind?
That's just it; I don't know if the things I'm reading mean that, or
what they seem to say.
Try it yourself; google for supersymmetry +translation and you'll
get any number of hits containing phrases like this:
"Since two supersymmetry transformations lead to a spacetime
translation, supersymmetry can be thought of as the 'square root' of a
translation."
found at:
http://www.hep.fsu.edu/seeking_susy.html
or this:
"Supersymmetry translates fermions into bosons and vice versa. In
particular, it turns out that the net result of two consecutive
supersymmetry operations is simply a translation in space-time."
found here:
http://feynman.physics.lsa.umich.edu/~mduff/talks/1988%20-%20The%20Membrane%20at%20the%20End%20of%20the%20Universe/index.html
Those are simplistic examples; others are more detailed but that's
the general drift.
I was wondering if the actual idea was that SuSy explains the
problem of continuous motion in a quantized universe by recasting
infinitesimal motions as SuSy transformations from localizable
particles to unlocalizable superpartners, then back to localizable
particles slightly displaced from the previous location at a slightly
later time, but I'm not seeing that either.
If I find the time I will think about this question in the hope of
coming up with a more satisfactory answer.
I'd appreciate it greatly.
I'm looking for a definite resolution of this issue, and if my
interpretation is physically correct some more details like how great
a displacement we're talking about and how long it takes, not to
mention whether or not other particles need be involved. I believe the
answer to the last is "no" ("virtual" neutralinos or gravitinos may
need to be emitted and reabsorbed to account for the 1/2 spin change),
but again I'm rather at sea here.
I wish I knew where else to ask. Yours is the sole response I've
gotten here; everyone else seems to want to rehash old versions of
Relativity, and misinterpret near-field EM as FTL. ;>)
Mark L. Fergerson
.
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| User: "" |
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| Title: Re: Supersymmetry Question |
02 Apr 2007 03:10:54 AM |
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On 2 Apr, 07:47, "n...@bid.ness" <Alien8...@gmail.com> wrote:
On Apr 1, 3:39 pm, wrote:
On 1 Apr, 06:59, "n...@bid.ness" <Alien8...@gmail.com> wrote:
I am under the impression that under Supersymmetry, transforming a
particle to its superpartner and back (electron->selectron->electron)
leaves the particle unchanged but displaced physically. Is this still
considered correct, or not? If so, is this displacement visible in
ordinary spacetime, or in one or more of the "extra" dimensions
presumed required for Supersymmetry?
Well the first thing I should say is that extra dimensions are *not*
required for supersymmetry; indeed most introductory courses teach
supersymmetry in 3+1 dimensions (this turns out to be a relatively
easy case due to the nice relationship between the Lorentz group and
its double cover, as well as being physically relevant). SuperSTRING
theory requires extra dimensions for reasons I couldn't claim to
understand, but one can perfectly well consider ordinary field
theories which are supersymmetric.
I've been Googling SuSy for a couple days and indeed get the
impression that it is currently (considering it's been blended into
superstring theory) thought to require more than 3+1 spacetime
dimensions, though I could easily have that wrong.
Well as I wrote before, one can certainly consider toy models that are
3+1 dimensional supersymmetric field theories. It may be the case that
such models are ruled out by experiment and that *realistic*
supersymmetric theories need extra dimensions, but I'm not aware of
this (but then I don't know anything about phenomenology so there's no
reason I would be). Can you provide links to where you read this?
As for the rest of your question, I'm not sure that it makes sense. I
think that you may be confusing supersymmetry transformations (which
are a group of symmetries of a theory) with the generators Q and Qbar
of those transformations. Q or Qbar acts on a bosonic state to give a
fermionic state and vice-versa, but a supersymmetry transformation
acting on an electron will leave the system in a mixed state with both
electron and selectron. Since the transformations form a group, any
two supersymmetry transformations performed one after the other are
the same as a single supersymmetry transformation, so talking about a
supersymmetry transformation followed by another is redundant. In
particular to any transformation there is an inverse, so one can
transform an electron into a mixed state and back again without
changing a thing.
The mixed state thing I have not yet run across and is entirely "who
ordered that!?" undesired. Oh, well.
Also yes, in the event of a transformation and its inverse being
applied sequentially nothing changes except the location of the
particle, at least that's what I think I'm reading.
If by transformation you mean "group element" then a transformation
followed by its inverse leaves everything, including location,
unchanged. This is the definition of "inverse".
If we act on an electron twice with generators epsilon*Q +
epsilonbar*Qbar I think that we get back some linear combination of
the momenta operators acting on the electron; since momentum is the
generator of translations, perhaps this is what you have in mind?
That's just it; I don't know if the things I'm reading mean that
I think they do. To understand the distinction between group elements
and generators, consider the example of U(1), which may be thought of
as the multiplicative group of complex numbers with absolute value 1.
An element of this group is of the form u = exp(i*a) for some real
number a. Suppose that this group acts on some set by multiplication,
i.e. x |--> u*x. Now, abandoning rigour, consider such a u which is
"infinitely close" to the identity, so that u = 1 + i*delta for some
"infinitesimal" real number delta. Multiplication of u by its complex
conjugate shows that such a u is indeed an element of U(1) provided we
ignore the term delta^2 on the grounds that it is tiny. Then if we act
on some x with this u, we find that x changes by an amount i*delta*x.
In this analogy, the i*delta corresponds to i*(epsilon*Q +
epsilonbar*Qbar); it is the change in the state of the system under an
"infinitesimal" supersymmetry transformation. (Sorry if the preceding
discussion was patronising, I have no idea how much you know).
Therefore, what the references are saying is that under two such
infinitesimal supersymmetry transformations acting on, say, a
fermionic state, the total change in the state is the sum of the
individual changes from each transformation (which are bosonic) plus
an infinitesimal linear combination of momenta acting on the original
state. Since momenta are the generators of translations, the original
state plus momenta acting on the original state are an infinitesimal
translation of the original state (in fact a transformation in
superspace).
Try it yourself; google for supersymmetry +translation and you'll
get any number of hits containing phrases like this:
"Since two supersymmetry transformations lead to a spacetime
translation, supersymmetry can be thought of as the 'square root' of a
translation."
found at:
http://www.hep.fsu.edu/seeking_susy.html
OK, it looks like I owe you an apology: it seems that some people use
the word "transformation" differently to how I use it. The
transformations to which this quote is referring are the generators I
wrote about above. Note that in a supersymmetric theory, the laws of
physics are invariant if all fields are transformed by a group
element. They are not invariant if all fields are acted on by the kind
of transformation described here, but are invariant if all fields are
replaced by their original value PLUS the change due to the action of
the generators, provided the generators are infinitessimal.
I was wondering if the actual idea was that SuSy explains the
problem of continuous motion in a quantized universe by recasting
infinitesimal motions as SuSy transformations from localizable
particles to unlocalizable superpartners, then back to localizable
particles slightly displaced from the previous location at a slightly
later time, but I'm not seeing that either.
I don't see how that "explains the problem", in fact I don't see how
the problem needs explaining.
If I find the time I will think about this question in the hope of
coming up with a more satisfactory answer.
I'd appreciate it greatly.
On reflection I'm not sure what else I can write apart from just
reproducing formulae from the books; the thing about supersymmetry is
that it really isn't a subject that lends itself to intuitive
explanations, one really needs to just look at the equations. I can
recommend this introductory article, if you do wish to learn about the
subject:
http://uk.arxiv.org/PS_cache/hep-th/pdf/0101/0101055.pdf
I'm looking for a definite resolution of this issue, and if my
interpretation is physically correct some more details like how great
a displacement we're talking about and how long it takes,
I don't think that "how long it takes" is meaningful. Supersymmetry
transformations are abstract things, not something one does; I don't
think that one can perform one in the same way that one can perform,
say, a rotation.
not to
mention whether or not other particles need be involved. I believe the
answer to the last is "no" ("virtual" neutralinos or gravitinos may
need to be emitted and reabsorbed to account for the 1/2 spin change),
but again I'm rather at sea here.
I wish I knew where else to ask. Yours is the sole response I've
gotten here; everyone else seems to want to rehash old versions of
Relativity, and misinterpret near-field EM as FTL. ;>)
Let me know if what I have written here is helpful.
-Rotwang
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| User: "Bob Cain" |
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| Title: Re: Supersymmetry Question |
02 Apr 2007 01:18:41 PM |
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wrote:
If by transformation you mean "group element" then a transformation
followed by its inverse leaves everything, including location,
unchanged. This is the definition of "inverse".
My comment may be more simplistic than it is simple but since you are
discussing consecutive transformations there will always be a
translation in time and, if there is observer motion relative to the
object transformed, in his space-time.
Bob
--
"Things should be described as simply as possible, but no simpler."
A. Einstein
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| User: "" |
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| Title: Re: Supersymmetry Question |
02 Apr 2007 02:45:45 PM |
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On Apr 2, 11:18 am, Bob Cain <arc...@arcanemethods.com> wrote:
s...@hotmail.co.uk wrote:
If by transformation you mean "group element" then a transformation
followed by its inverse leaves everything, including location,
unchanged. This is the definition of "inverse".
My comment may be more simplistic than it is simple but since you are
discussing consecutive transformations there will always be a
translation in time and, if there is observer motion relative to the
object transformed, in his space-time.
I have no problem with "simplistic", that being the level of the
stuff I cited.
However your caveat that there must be relative motion does not
appear anywhere I've seen; the implication is that displacement due to
consecutive transformations is relative to the particle's own idea of
what "here" means.
Mark L. Fergerson
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| User: "Bob Cain" |
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| Title: Re: Supersymmetry Question |
04 Apr 2007 06:33:42 PM |
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wrote:
On Apr 2, 11:18 am, Bob Cain <arc...@arcanemethods.com> wrote:
s...@hotmail.co.uk wrote:
If by transformation you mean "group element" then a transformation
followed by its inverse leaves everything, including location,
unchanged. This is the definition of "inverse".
My comment may be more simplistic than it is simple but since you are
discussing consecutive transformations there will always be a
translation in time and, if there is observer motion relative to the
object transformed, in his space-time.
I have no problem with "simplistic", that being the level of the
stuff I cited.
However your caveat that there must be relative motion does not
appear anywhere I've seen; the implication is that displacement due to
consecutive transformations is relative to the particle's own idea of
what "here" means.
The only real caveat is that there be a space-time interval. This is
required by the fact that the transformations are consecutive. How
that is decomposed along coordinates is just an observer dependency.
Bob
--
"Things should be described as simply as possible, but no simpler."
A. Einstein
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| User: "Timothy Golden BandTechnology.com" |
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| Title: Re: Supersymmetry Question |
03 Apr 2007 07:48:21 AM |
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On Apr 2, 3:45 pm, "n...@bid.ness" <Alien8...@gmail.com> wrote:
On Apr 2, 11:18 am, Bob Cain <arc...@arcanemethods.com> wrote:
s...@hotmail.co.uk wrote:
If by transformation you mean "group element" then a transformation
followed by its inverse leaves everything, including location,
unchanged. This is the definition of "inverse".
My comment may be more simplistic than it is simple but since you are
discussing consecutive transformations there will always be a
translation in time and, if there is observer motion relative to the
object transformed, in his space-time.
I have no problem with "simplistic", that being the level of the
stuff I cited.
However your caveat that there must be relative motion does not
appear anywhere I've seen; the implication is that displacement due to
consecutive transformations is relative to the particle's own idea of
what "here" means.
Mark L. Fergerson
Hi Mark. I am curious what you think of electron spin and spin
filtration. The concept of yielding a spin polarized stream is not
apparently a reality; as the purity is driven up the population
diminishes:
http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-6606.pdf
Figure 5 exposes the behavior. The best they can do is 85% and the
intensity diminishes at this highest value.
Elsewhere on the web we see Stern-Gerlach like magnet setups that form
spin filtration mechanisms. I do not believe these are a reality are
they? Since you are a good critical reader willing to be skeptical I
thought I'd see if you have an opinion.
The way that I see the particle models is that they play these
mathematical spaces out not as additional dimensions but as rules of
particle logic that apply to particles who are positioned in
spacetime. It is a large collage of such rules that builds the model.
I am not knowledgable on superpartner particles so I apologize for not
having a direct answer. Still, spin came up in one of the posts here
so I thought I'd throw this tangential question at you. Awhile back I
delved into it and the reference I give was one of the most
impressive. Spin has been accepted yet its interpretation still awaits
a clean arrival. I think the binary quality is oversimplified. It is
hard to believe that I sincerely believe this with all of spintronics
going on, but it hasn't happened yet has it? Will they suffer the same
85% binary accuracy?
-Tim
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| User: "" |
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| Title: Re: Supersymmetry Question |
05 Apr 2007 03:41:01 AM |
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On Apr 3, 5:48 am, "Timothy Golden BandTechnology.com"
<tttppp...@yahoo.com> wrote:
On Apr 2, 3:45 pm, "n...@bid.ness" <Alien8...@gmail.com> wrote:
Hi Mark. I am curious what you think of electron spin and spin
filtration. The concept of yielding a spin polarized stream is not
apparently a reality; as the purity is driven up the population
diminishes:
http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-6606.pdf
Figure 5 exposes the behavior. The best they can do is 85% and the
intensity diminishes at this highest value.
AFAICT they're at the intersection of several competing limits of
diminishing returns. See this:
http://www.osti.gov/bridge/servlets/purl/859311-Ne8ltA/859311.PDF
Part 2 (pp 4-10) mostly.
The structure can't reach theoretical perfection for several
reasons, mainly that the damned lattice won't hold still. It would
help if it could be operated while very cold, but it can't.
They could get more current by using a larger area with the low
current/area required to achieve high QE, but the beam would have to
be reduced in diameter downstream. That essentially means having to
shave off those electrons that acquired transverse momentum in the
process; think billiards- you want nice, solid centerline kisses, not
off-center slaps.
Elsewhere on the web we see Stern-Gerlach like magnet setups that form
spin filtration mechanisms. I do not believe these are a reality are
they? Since you are a good critical reader willing to be skeptical I
thought I'd see if you have an opinion.
Yes they _work_, but such setups can never meet the requirements for
a high-energy accelerator source; they produce curved beams that would
have to be straightened for acceleration which would again introduce
transverse energy components that would have to be shaved off.
The way that I see the particle models is that they play these
mathematical spaces out not as additional dimensions but as rules of
particle logic that apply to particles who are positioned in
spacetime. It is a large collage of such rules that builds the model.
So far the models work pretty well; the cited sources could not have
been imagined, much less embodied as well as they have been, if the
models were very deeply flawed.
Spin has been accepted yet its interpretation still awaits
a clean arrival. I think the binary quality is oversimplified. It is
hard to believe that I sincerely believe this with all of spintronics
going on, but it hasn't happened yet has it? Will they suffer the same
85% binary accuracy?
Um. Stern-Gerlach itself fairly solidly supports the binary quality
of spin. It also demonstrates the _possibiliity_ of greater spin
selectivity than the cited cathode structures. However any physical
process that selects a desired property from a mixture will inevitably
introduce some other limitations; it's always a matter of compromise.
If I was tasked to produce an intense polarized electron beam with
good quantum efficiency I'd start with a physical process that
efficiently produces _only_ electrons of the desired polarization,
then work on the brightness. I'd probably not start from the particle
perspective but from the wave perspective; find a material that
preferentially internally propagates only one polarization state of
electron waves, then figure out how to extract them. Notice that the
cited lattices can be seen as a limited sort of metamaterial, which
are generally known for exhibiting what's called "handedness" when
passing EM waves of differing polarizations preferentially. However
the lattice's main limitation in that view isn't at the surface but
internally; it starts with electrons of all orientations and
progressively filters them on the way out and each step adds its
increment of trouble. Working with matter wave phenomena of course
means working cold to get usably long wavelengths, but it wouldn't be
under the same kinds of temperature regime restrictions as the cited
tech.
Mark L. Fergerson
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| User: "Timothy Golden BandTechnology.com" |
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| Title: Re: Supersymmetry Question |
06 Apr 2007 09:14:12 AM |
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On Apr 5, 4:41 am, "n...@bid.ness" <Alien8...@gmail.com> wrote:
On Apr 3, 5:48 am, "Timothy Golden BandTechnology.com"
<tttppp...@yahoo.com> wrote:
On Apr 2, 3:45 pm, "n...@bid.ness" <Alien8...@gmail.com> wrote:
Hi Mark. I am curious what you think of electron spin and spin
filtration. The concept of yielding a spin polarized stream is not
apparently a reality; as the purity is driven up the population
diminishes:
http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-6606.pdf
Figure 5 exposes the behavior. The best they can do is 85% and the
intensity diminishes at this highest value.
AFAICT they're at the intersection of several competing limits of
diminishing returns. See this:
http://www.osti.gov/bridge/servlets/purl/859311-Ne8ltA/859311.PDF
Part 2 (pp 4-10) mostly.
The structure can't reach theoretical perfection for several
reasons, mainly that the damned lattice won't hold still. It would
help if it could be operated while very cold, but it can't.
Thanks for the excellent link. Your link does site a 100% theoretical
limit. I can accept the compromise argument you make but I don't see
the situation as clearly as you. The indirect nature of these
experiments leaves the compromise as much in the theory as it may be
in the experiment.
They could get more current by using a larger area with the low
current/area required to achieve high QE, but the beam would have to
be reduced in diameter downstream. That essentially means having to
shave off those electrons that acquired transverse momentum in the
process; think billiards- you want nice, solid centerline kisses, not
off-center slaps.
Elsewhere on the web we see Stern-Gerlach like magnet setups that form
spin filtration mechanisms. I do not believe these are a reality are
they? Since you are a good critical reader willing to be skeptical I
thought I'd see if you have an opinion.
Yes they _work_, but such setups can never meet the requirements for
a high-energy accelerator source; they produce curved beams that would
have to be straightened for acceleration which would again introduce
transverse energy components that would have to be shaved off.
The way that I see the particle models is that they play these
mathematical spaces out not as additional dimensions but as rules of
particle logic that apply to particles who are positioned in
spacetime. It is a large collage of such rules that builds the model.
So far the models work pretty well; the cited sources could not have
been imagined, much less embodied as well as they have been, if the
models were very deeply flawed.
Well this brings up their means of measuring the polarized stream as
well. I have not focused on that end of the experiment which is as
important as the claim of generation. I am happy to attribute more
qualities to the electron than just charge but the spin model is very
confusing and as I attempt to understand it I land in this unsettled
space that I am trying to communicate. The desire to attribute
geometry to the electron's inherent qualities is irresistible as can
be seen in the seven hundred twenty degrees of freedom that some like
to think of the discrete up/down theory in.
Spin has been accepted yet its interpretation still awaits
a clean arrival. I think the binary quality is oversimplified. It is
hard to believe that I sincerely believe this with all of spintronics
going on, but it hasn't happened yet has it? Will they suffer the same
85% binary accuracy?
Um. Stern-Gerlach itself fairly solidly supports the binary quality
of spin. It also demonstrates the _possibiliity_ of greater spin
selectivity than the cited cathode structures. However any physical
process that selects a desired property from a mixture will inevitably
introduce some other limitations; it's always a matter of compromise.
Stern-Gerlach used hot silver atoms and apparently now potassium is
used. When they attempted the experiment with a pinhole the image was
so poor that they had to open up the pinhole to a slot. The image has
some odd details. I studied this carefully some time ago and came away
with my skepticism not satiated due to the indirect nature of the
experiment. Indirection seems to be key to detection and the struggle
to form a belief then leaves the problem open.
There are magnetic fields which yield circular orbits for electrons
which employ the same orientation field as used in SG. Though not
inhomogeneous couldn't such a circular Stern-Gerlach be performed on
the electron? The electrons would whip around and what? The weaker
side of the field will pull some electrons over that way and the
stronger side pulls them the other way? This is not acceptable from
the principles of symmetry. Assigning the electron a magnetic moment
in addition to the traditional charge quality does not fully answer
and as I visualize these concepts anisotropic properties would allow
for some of the behaviors such that a broken symmetry in the electron
would yield a balance with the broken symmetry of the magnetic field.
In effect this boils down to allowing an electron's magnetic moment to
contain a focused pole whereby its unfocused pole is practically
nonexistent. A discrete magnetic flux then always exits the focus but
reenters just about anywhere. There is a natural model of this in the
Mandelbrot set when studying orbital qualities of the stable set,
though the focus is not so precise as I suggest here and the return
paths are not arbitrary. So something close to this model does exist
in primitive mathematics.
For this style model to portray spin it will require the allotment of
the focus changing from North to South and such a procedure need not
be discrete. The continuous change over may be more in line with some
of the cold physics, which is exposing 2D electron behaviors. These 2D
conditions won't portray its electrons as distinguishable via the
binary up/down characterization according to this focus model. At this
2D stage the transition from up to down is happening and the magnetic
behavior of the electron would be perfect; exhibiting a bar magnet
type of behavior. Will charge even be present in this form? I don't
know, but playing with this sort of model is far more interesting than
puzzling over a geometry involving 720 degrees that is a continuous
geometry that is supposed to portray a discrete behavior. In this new
paradigm we effectively have the electron turning itself inside out
and so the continuous behavior can be resolved to discrete up/down
dichotomy though we would readily admit an indeterminate state at the
transition.
http://bandtechnology.com/PolySigned/Deformation/AxisDualDeformStudy.gif
exposes a natural inside out product behavior in 3D. This can be
resolved as an improper transform in matrix mathematics, or rather a
continuous projection from proper to improper. The middle state is a
necessary 2D state within a 3D inversion. The 1D extreme should also
be of interest perhaps to tunneling.
As my model is simplistic I hope you understand it. The weirdness of
magnetic moment even suggests that a standard dipole magnet negatively
charged would show more up electrons at one end and more down
electrons at the other. I suppose as models are supposed to predict
something that this is a predictor of the anisotropic electron model's
accuracy.
If I was tasked to produce an intense polarized electron beam with
good quantum efficiency I'd start with a physical process that
efficiently produces _only_ electrons of the desired polarization,
then work on the brightness. I'd probably not start from the particle
perspective but from the wave perspective; find a material that
preferentially internally propagates only one polarization state of
electron waves, then figure out how to extract them. Notice that the
cited lattices can be seen as a limited sort of metamaterial, which
are generally known for exhibiting what's called "handedness" when
passing EM waves of differing polarizations preferentially. However
the lattice's main limitation in that view isn't at the surface but
internally; it starts with electrons of all orientations and
progressively filters them on the way out and each step adds its
increment of trouble. Working with matter wave phenomena of course
means working cold to get usably long wavelengths, but it wouldn't be
under the same kinds of temperature regime restrictions as the cited
tech.
Mark L. Fergerson
Thanks Mark. You have the best understanding of this topic that I have
seen on usenet and so I appreciate your detailed response. I am
reading and receiving your arguments of consistency but attempt to
allow the problem some open space. Particularly in the area of spin
transition I have little understanding of the experimental or
theoretical control that is possible and perhaps that would be a
helpful direction to extend this conversation. This must tie back to
the polarization problem. The shavings that you talk about are of
continuous nature in the 720 degree sense right? But then what of the
discrete up/down? Is it continuous or is it discrete? My proposal is
that it is a dichotomy with an indeterminate middle that may be
consistent with some dimensional electron behaviors at low
temperature.
-Tim
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| User: "" |
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| Title: Re: Supersymmetry Question |
02 Apr 2007 04:41:08 PM |
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On Apr 2, 1:10 am, wrote:
On 2 Apr, 07:47, "n...@bid.ness" <Alien8...@gmail.com> wrote:
On Apr 1, 3:39 pm, wrote:
On 1 Apr, 06:59, "n...@bid.ness" <Alien8...@gmail.com> wrote:
I am under the impression that under Supersymmetry, transforming a
particle to its superpartner and back (electron->selectron->electro=
n)
leaves the particle unchanged but displaced physically. Is this sti=
ll
considered correct, or not? If so, is this displacement visible in
ordinary spacetime, or in one or more of the "extra" dimensions
presumed required for Supersymmetry?
Well the first thing I should say is that extra dimensions are *not*
required for supersymmetry; indeed most introductory courses teach
supersymmetry in 3+1 dimensions (this turns out to be a relatively
easy case due to the nice relationship between the Lorentz group and
its double cover, as well as being physically relevant). SuperSTRING
theory requires extra dimensions for reasons I couldn't claim to
understand, but one can perfectly well consider ordinary field
theories which are supersymmetric.
I've been Googling SuSy for a couple days and indeed get the
impression that it is currently (considering it's been blended into
superstring theory) thought to require more than 3+1 spacetime
dimensions, though I could easily have that wrong.
Well as I wrote before, one can certainly consider toy models that are
3+1 dimensional supersymmetric field theories. It may be the case that
such models are ruled out by experiment and that *realistic*
supersymmetric theories need extra dimensions, but I'm not aware of
this (but then I don't know anything about phenomenology so there's no
reason I would be). Can you provide links to where you read this?
Not off the top of my head. My impression of the current state of
the SuSy/superstring connection is somewhat confused as there don't
seem to be many recent papers available that are accessible to someone
at my level of comprehension.
As for the rest of your question, I'm not sure that it makes sense. I
think that you may be confusing supersymmetry transformations (which
are a group of symmetries of a theory) with the generators Q and Qbar
of those transformations. Q or Qbar acts on a bosonic state to give a
fermionic state and vice-versa, but a supersymmetry transformation
acting on an electron will leave the system in a mixed state with both
electron and selectron. Since the transformations form a group, any
two supersymmetry transformations performed one after the other are
the same as a single supersymmetry transformation, so talking about a
supersymmetry transformation followed by another is redundant. In
particular to any transformation there is an inverse, so one can
transform an electron into a mixed state and back again without
changing a thing.
The mixed state thing I have not yet run across and is entirely "who
ordered that!?" undesired. Oh, well.
I'm looking into that and struggling mightily.
Also yes, in the event of a transformation and its inverse being
applied sequentially nothing changes except the location of the
particle, at least that's what I think I'm reading.
If by transformation you mean "group element" then a transformation
followed by its inverse leaves everything, including location,
unchanged. This is the definition of "inverse".
If we act on an electron twice with generators epsilon*Q +
epsilonbar*Qbar I think that we get back some linear combination of
the momenta operators acting on the electron; since momentum is the
generator of translations, perhaps this is what you have in mind?
That's just it; I don't know if the things I'm reading mean that
I think they do. To understand the distinction between group elements
and generators, consider the example of U(1), which may be thought of
as the multiplicative group of complex numbers with absolute value 1.
An element of this group is of the form u =3D exp(i*a) for some real
number a. Suppose that this group acts on some set by multiplication,
i.e. x |--> u*x. Now, abandoning rigour, consider such a u which is
"infinitely close" to the identity, so that u =3D 1 + i*delta for some
"infinitesimal" real number delta. Multiplication of u by its complex
conjugate shows that such a u is indeed an element of U(1) provided we
ignore the term delta^2 on the grounds that it is tiny. Then if we act
on some x with this u, we find that x changes by an amount i*delta*x.
In this analogy, the i*delta corresponds to i*(epsilon*Q +
epsilonbar*Qbar); it is the change in the state of the system under an
"infinitesimal" supersymmetry transformation. (Sorry if the preceding
discussion was patronising, I have no idea how much you know).
Evidently much less than you might think; I am not a mathematician,
merely an interested layman.
Please don't worry about patronizing me. I consider humility and
humiliation two very different things.
To clarify, I breezed through trig and geometry but hit a wall at
calculus because I could not get an instructor to make me see why it
was more useful than other physically usable methods.
Your above explanation makes perfect sense to me, but is completely
at odds with the cites I keep quoting; I would expect a complex-valued
quantity to have the same value before and after any pair of inversely-
related operations, yet the cites tell me I must expect the before and
after values to change slightly. I see it as equivalent to telling me
that if I take a CW RF signal and digitize it, take the cosine, then
take the sine of that, the resulting signal will be different from the
original by some small phase angle not related to hardware-induced
lags which is empirically false.
Therefore, what the references are saying is that under two such
infinitesimal supersymmetry transformations acting on, say, a
fermionic state, the total change in the state is the sum of the
individual changes from each transformation (which are bosonic) plus
an infinitesimal linear combination of momenta acting on the original
state. Since momenta are the generators of translations, the original
state plus momenta acting on the original state are an infinitesimal
translation of the original state (in fact a transformation in
superspace).
Try it yourself; google for supersymmetry +translation and you'll
get any number of hits containing phrases like this:
"Since two supersymmetry transformations lead to a spacetime
translation, supersymmetry can be thought of as the 'square root' of a
translation."
found at:
http://www.hep.fsu.edu/seeking_susy.html
OK, it looks like I owe you an apology: it seems that some people use
the word "transformation" differently to how I use it. The
transformations to which this quote is referring are the generators I
wrote about above. Note that in a supersymmetric theory, the laws of
physics are invariant if all fields are transformed by a group
element. They are not invariant if all fields are acted on by the kind
of transformation described here, but are invariant if all fields are
replaced by their original value PLUS the change due to the action of
the generators, provided the generators are infinitessimal.
From what I'm extracting from what I've read, these transformations
are to be taken as globally valid but are to be only applied locally.
I have no problem with that even though I am uncomfortable with
idealizations that prohibit real-world workarounds for instance taking
measurements at more than one location in the Elevator
Gedankenexperiment.
I was wondering if the actual idea was that SuSy explains the
problem of continuous motion in a quantized universe by recasting
infinitesimal motions as SuSy transformations from localizable
particles to unlocalizable superpartners, then back to localizable
particles slightly displaced from the previous location at a slightly
later time, but I'm not seeing that either.
I don't see how that "explains the problem", in fact I don't see how
the problem needs explaining.
Never mind, just a brainfart of mine.
If I find the time I will think about this question in the hope of
coming up with a more satisfactory answer.
I'd appreciate it greatly.
On reflection I'm not sure what else I can write apart from just
reproducing formulae from the books; the thing about supersymmetry is
that it really isn't a subject that lends itself to intuitive
explanations, one really needs to just look at the equations. I can
recommend this introductory article, if you do wish to learn about the
subject:
http://uk.arxiv.org/PS_cache/hep-th/pdf/0101/0101055.pdf
Notice on page 18 this:
"We now want to realise the susy generators Q=CE=B1 and their hermitian
conjugates
Q=CE=B1=CB=99 =3D (Q=CE=B1)=E2=80=A0 as differential operators on superspac=
e=2E We want that
i=C7=AB=CE=B1Q=CE=B1 generates
a translation in =CE=B8=CE=B1 by a constant infinitesimal spinor =C7=AB=CE=
=B1 plus some
translation
in x=CE=BC. The latter space-time translation is determined by the susy
algebra since
the commutator of two such susy transformations is a translation in
space-time."
(symbols didn't translate all that well from PDF to ascii)
Again, it is implied (OK, maybe I'm just inferring) that the
mathematics says that there is a physically real displacement.
I cheerfully admit to working from an intuitive mindset, though I am
constantly on guard against it. Also I'm of the possibly inflated
opinion that my intuition is not Newtonian but rather post-
Einsteinian. I am somewhat more comfortable with the concept that what
appears to be abstract math can have physically real, though not
easily observable at human scales, consequences than are average
laymen.
OTOH I may be _too_ ready to assume the latter; when authors of the
papers we've been citing at each other descend from abstract math and
make statements in what appears to be plain English, I may be taking
them a tad too literally. Yet there does seem to be a consensus...
I'm looking for a definite resolution of this issue, and if my
interpretation is physically correct some more details like how great
a displacement we're talking about and how long it takes,
I don't think that "how long it takes" is meaningful. Supersymmetry
transformations are abstract things, not something one does; I don't
think that one can perform one in the same way that one can perform,
say, a rotation.
Is there then no supposed physical meaning to the math? I was under
the impression (there goes my intuition again) that the possibility of
physically realizing mathematical implications like this is what
drives relatively recent proposals for instance to directly detect
axions using strong magnetic fields to "transform" them into photons,
including engineering details like how strong the magnetic fields need
to be, and where to place what sorts of detectors.
See, I come from an engineering mindset, and take as given that
theorists won't put decades of effort into something like SuSy if they
don't believe it has potential hardware-testable applications
somewhere down the line.
not to
mention whether or not other particles need be involved. I believe the
answer to the last is "no" ("virtual" neutralinos or gravitinos may
need to be emitted and reabsorbed to account for the 1/2 spin change),
but again I'm rather at sea here.
I wish I knew where else to ask. Yours is the sole response I've
gotten here; everyone else seems to want to rehash old versions of
Relativity, and misinterpret near-field EM as FTL. ;>)
Let me know if what I have written here is helpful.
To some degree; mentioning the "mixed state" has given me another
line of research. OTOH you might not be able to explain things any
better to me as I simply don't have the mathematical facility to
follow the more abstract details; I'm still, despite my intuition,
trying to figure out how to concretize the concepts.
Mark L. Fergerson
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| User: "" |
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| Title: Re: Supersymmetry Question |
08 Apr 2007 03:36:10 PM |
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Sorry I've taken so long to reply to this. This is the first time in
the last few days that I've had a chance to sit in front of a computer
for any great length of time.
On 2 Apr, 22:41, "n...@bid.ness" <Alien8...@gmail.com> wrote:
[me]
If we act on an electron twice with generators epsilon*Q +
epsilonbar*Qbar I think that we get back some linear combination of
the momenta operators acting on the electron; since momentum is the
generator of translations, perhaps this is what you have in mind?
That's just it; I don't know if the things I'm reading mean that
I think they do. To understand the distinction between group elements
and generators, consider the example of U(1), which may be thought of
as the multiplicative group of complex numbers with absolute value 1.
An element of this group is of the form u =3D exp(i*a) for some real
number a. Suppose that this group acts on some set by multiplication,
i.e. x |--> u*x. Now, abandoning rigour, consider such a u which is
"infinitely close" to the identity, so that u =3D 1 + i*delta for some
"infinitesimal" real number delta. Multiplication of u by its complex
conjugate shows that such a u is indeed an element of U(1) provided we
ignore the term delta^2 on the grounds that it is tiny. Then if we act
on some x with this u, we find that x changes by an amount i*delta*x.
In this analogy, the i*delta corresponds to i*(epsilon*Q +
epsilonbar*Qbar); it is the change in the state of the system under an
"infinitesimal" supersymmetry transformation. (Sorry if the preceding
discussion was patronising, I have no idea how much you know).
[...]
Your above explanation makes perfect sense to me, but is completely
at odds with the cites I keep quoting; I would expect a complex-valued
quantity to have the same value before and after any pair of inversely-
related operations, yet the cites tell me I must expect the before and
after values to change slightly.
There is no contradiction here. The point is that we are talking about
two distinct types of operation on the space of fields: the operation
of multiplication by a group element, and the operation of
multiplication by a generator. In the U(1) analogy I used above these
two operations correspond to x |--> exp(i*delta)*x and x |--> delta*x
respectively. The group elements are invertible, and operating on a
state by a group element followed by its inverse will indeed leave the
state unchanged. However the cites you quote are referring to the
second type of operation, multiplication by generators. In fact the
supersymmetry generators Q and Qbar are *not* invertible.
I see it as equivalent to telling me
that if I take a CW RF signal and digitize it, take the cosine, then
take the sine of that, the resulting signal will be different from the
original by some small phase angle not related to hardware-induced
lags which is empirically false.
I'm afraid I don't know what a CW RF signal is.
From what I'm extracting from what I've read, these transformations
are to be taken as globally valid but are to be only applied locally.
Not sure what you mean by this. Can you give a reference?
http://uk.arxiv.org/PS_cache/hep-th/pdf/0101/0101055.pdf
Notice on page 18 this:
"We now want to realise the susy generators Q=CE=B1 and their hermitian
conjugates
Q=CE=B1=CB=99 =3D (Q=CE=B1)=E2=80=A0 as differential operators on supersp=
ace. We want that
i=C7=AB=CE=B1Q=CE=B1 generates
a translation in =CE=B8=CE=B1 by a constant infinitesimal spinor =C7=AB=
=CE=B1 plus some
translation
in x=CE=BC. The latter space-time translation is determined by the susy
algebra since
the commutator of two such susy transformations is a translation in
space-time."
(symbols didn't translate all that well from PDF to ascii)
Note that the quote refers to the "susy generators". Note also that
the quantity i*epsilon^a*Q_a is a sum of terms involving a single
generator Q_a; the quote is saying that the action of a *single*
generator involves a spacetime translation (on a superfield), which is
required in order that the generators satisfy the susy algebra (which
roughly states that, as you wrote before, the Q's should be a "square
root" of the momentum).
Again, it is implied (OK, maybe I'm just inferring) that the
mathematics says that there is a physically real displacement.
I'm not sure what you mean by "physically real displacement" here.
Superfields are functions of both commuting coordinates (corresponding
to spacetime) and anticommuting coordinates; they are really just a
mathematical trick to collect a load of different fields into one
easily managed whole, in much the same way as three component vector
notation is a neat way of treating the three components of the
electric field as one. The quote is saying that the value of the susy-
transformed superfield at a given point in superspace depends on the
value of the original superfield at a displaced point in superspace.
In particular, looking at equation 4.7, the spacetime coordinates are
translated by a quantity which is not a real number but rather a
Grassmann number, so in that sense the translation is not physically
real.
Is there then no supposed physical meaning to the math?
Well there is certainly physical meaning to it, it just isn't meaning
that lends itself to nice intuitive descriptions in the same way that
the maths of say, general relativity does. I guess that at the end of
the day the meaning of supersymmetry just isn't that exciting from the
point of view of a layman; what susy is saying (if it exists) is that
the laws of physics are invariant under certain transformations that
have no analogue with something that we experience in everyday life.
Physicists are interested in susy for technical reasons, such as the
fact that it makes theories renormalizable.
I was under
the impression (there goes my intuition again) that the possibility of
physically realizing mathematical implications like this is what
drives relatively recent proposals for instance to directly detect
axions using strong magnetic fields to "transform" them into photons,
including engineering details like how strong the magnetic fields need
to be, and where to place what sorts of detectors.
I have not heard of this, it sounds interesting. I was under the
impression that we could not physically realise susy transformations
in the same way that we can realise, say, rotations (by rotating our
aparatus) but from what you are saying it sounds like people might
have come up with a way to do so.
See, I come from an engineering mindset, and take as given that
theorists won't put decades of effort into something like SuSy if they
don't believe it has potential hardware-testable applications
somewhere down the line.
Well even if we can't physically realise susy transformations that
doesn't mean we can't test it! This is because the mere existence of
supersymmetry in a theory has many nice consequences. An obvious
example is that in a theory with unbroken susy, every particle is
paired with a sparticle of the same mass. A less obvious example is
that in a supersymmetric theory there are relations between coupling
constants which would be arbitrary in a non-supersymmetric theory.
To some degree; mentioning the "mixed state" has given me another
line of research.
Well you probably won't find many references to that in the sources
because they tend to concentrate on the action of the susy generators
without mentioning the actual group elements. If you have access to a
good library, you could try looking at chapters 3 and 4 of
"Supersymmetry and Supergravity" by Wess and Bagger, where the action
of group elements is explicity described. They are pretty technical
but you might be able get the gist without paying too much attention
to the details.
-Rotwang
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| User: "" |
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| Title: Re: Supersymmetry Question |
15 Apr 2007 03:19:35 AM |
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On Apr 8, 1:36 pm, wrote:
Sorry I've taken so long to reply to this. This is the first time in
the last few days that I've had a chance to sit in front of a computer
for any great length of time.
No problem; this is the first time I've been able to focus on this
long enough to respond. Thanks for your patience.
On 2 Apr, 22:41, "n...@bid.ness" <Alien8...@gmail.com> wrote:
(severe snip, Google groups is losing my posts right and left so I
want to be brief)
I was under
the impression (there goes my intuition again) that the possibility of
physically realizing mathematical implications like this is what
drives relatively recent proposals for instance to directly detect
axions using strong magnetic fields to "transform" them into photons,
including engineering details like how strong the magnetic fields need
to be, and where to place what sorts of detectors.
I have not heard of this, it sounds interesting. I was under the
impression that we could not physically realise susy transformations
in the same way that we can realise, say, rotations (by rotating our
aparatus) but from what you are saying it sounds like people might
have come up with a way to do so.
http://cast.web.cern.ch/CAST/
uses the Primakoff effect or process (for which Google).
For that matter Google for axion +detection and you'll see several
schemes based on Rydberg atoms transiting tuned cavities, a neat
"through-the-wall" idea for detecting axions produced in reactors and
accelerators, and so on. It seems to be one of the best candidates for
easy detection.
Anyway, if you have any ideas who else I might ask for clarification
of these statements that have my dander up, I'd appreciate it.
Mark L. Fergerson
PS BTW "CW RF" meant continuous wave radio frequency; a simple AC EM
signal.
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| User: "" |
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| Title: Re: Supersymmetry Question |
16 Apr 2007 09:59:17 AM |
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On 15 Apr, 09:19, "n...@bid.ness" <Alien8...@gmail.com> wrote:
Anyway, if you have any ideas who else I might ask for clarification
of these statements that have my dander up, I'd appreciate it.
I'm afraid I don't. Is there something specific in what I wrote which
needs to be explained better? I will reiterate my suggestion to have a
look at the book of Wess and Bagger if you are serious about
understanding supersymmetry (though be warned: you'll need to read
appendix A before you start at the beginning, a fact which is not
mentioned in the book).
-Rotwang
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