| Topic: |
Science > Physics |
| User: |
"Creighton Hogg" |
| Date: |
01 Jul 2004 05:29:15 PM |
| Object: |
Stupid questions |
This is one of those things that's occurred to me while waiting for
software to finish compiling.
Are there other valid frameworks for describing forces, at energy levels
~10TeV or lower, besides gauge interactions (I'm including string theory
here because at low energy the contact interactions of strings have to
look like gauge interactions)? I seem to remember being
told in a QFT class that you're not allowed to have any other kinds of
interactions, but I honestly don't understand why. I'm just wondering if
there's other options or if, at sufficiently low energy, everything *must*
look a QFT with gauge interactions.
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| User: "Thomas Dent" |
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| Title: Re: Stupid questions |
02 Jul 2004 06:09:30 AM |
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Creighton Hogg <wchogg@hep.wisc.edu> wrote
Are there other valid frameworks for describing forces, at energy levels
~10TeV or lower, besides gauge interactions (I'm including string theory
here because at low energy the contact interactions of strings have to
look like gauge interactions)? I seem to remember being
told in a QFT class that you're not allowed to have any other kinds of
interactions, but I honestly don't understand why. I'm just wondering if
there's other options or if, at sufficiently low energy, everything *must*
look a QFT with gauge interactions.
Why don't you ask one of the many particle theory professors at
Wisconsin? They don't bite. (At least, not all of them.)
It's certainly not true that you are *only* allowed gauge
interactions. Perhaps you are misremembering the QFT class. If you
have only fermions and vectors and restrict yourself to renormalizable
theories, then this is the case. (That is, if you don't count fermion
mass terms as 'interactions'.)
However you can have four-fermion (or 2n-fermion) interactions which
are not due to exchange of gauge bosons - they just turn out to be
nonrenormalizable in general. As Weinberg pointed out (1979), this is
not an automatic disaster. Nonrenormalizable theories can give useful
results if the cutoff is sufficiently high. For example the Fermi
theory works perfectly well at nuclear physics energies. And, of
course, gravity is nonrenormalizable.
If you allow scalar particles, the number of non-gauge interactions
increases markedly. At renormalizable level you have phi^3 and phi^4
operators and in general you can have phi^n and even operators with
derivatives (e.g. (d phi)^2 phi^2). Also Yukawa interactions (two
fermions and one scalar) which are renormalizable.
You can write down a perfectly good quantum field theory without any
gauge symmetry at all and without it being renormalizable and still
make some predictions. This is what chiral perturbation theory (Gasser
& Leutwyler 1984-1985) does, for example.
It is a different question as to what the *underlying* or
*fundamental* theory is. Since gravity exists, the underlying theory
cannot be just Yang-Mills. String models do tend to produce Yang-Mills
as a 4d low energy limit, but they also have a large scalar sector
which may include stuff which isn't constrained by 4d gauge symmetry.
Any further questions?
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| User: "Creighton Hogg" |
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| Title: Re: Stupid questions |
02 Jul 2004 10:19:15 AM |
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On 2 Jul 2004, Thomas Dent wrote:
Creighton Hogg <wchogg@hep.wisc.edu> wrote
Are there other valid frameworks for describing forces, at energy levels
~10TeV or lower, besides gauge interactions (I'm including string theory
here because at low energy the contact interactions of strings have to
look like gauge interactions)? I seem to remember being
told in a QFT class that you're not allowed to have any other kinds of
interactions, but I honestly don't understand why. I'm just wondering if
there's other options or if, at sufficiently low energy, everything *must*
look a QFT with gauge interactions.
Why don't you ask one of the many particle theory professors at
Wisconsin? They don't bite. (At least, not all of them.)
Yeah, I like all of the people I've met from the 5th floor. It's not
really a question for work, just my own idle musings, so I'd feel pretty
rude bugging them.
It's certainly not true that you are *only* allowed gauge
interactions. Perhaps you are misremembering the QFT class. If you
have only fermions and vectors and restrict yourself to renormalizable
theories, then this is the case. (That is, if you don't count fermion
mass terms as 'interactions'.)
However you can have four-fermion (or 2n-fermion) interactions which
are not due to exchange of gauge bosons - they just turn out to be
nonrenormalizable in general. As Weinberg pointed out (1979), this is
not an automatic disaster. Nonrenormalizable theories can give useful
results if the cutoff is sufficiently high. For example the Fermi
theory works perfectly well at nuclear physics energies. And, of
course, gravity is nonrenormalizable.
If you allow scalar particles, the number of non-gauge interactions
increases markedly. At renormalizable level you have phi^3 and phi^4
operators and in general you can have phi^n and even operators with
derivatives (e.g. (d phi)^2 phi^2). Also Yukawa interactions (two
fermions and one scalar) which are renormalizable.
You can write down a perfectly good quantum field theory without any
gauge symmetry at all and without it being renormalizable and still
make some predictions. This is what chiral perturbation theory (Gasser
& Leutwyler 1984-1985) does, for example.
It is a different question as to what the *underlying* or
*fundamental* theory is. Since gravity exists, the underlying theory
cannot be just Yang-Mills. String models do tend to produce Yang-Mills
as a 4d low energy limit, but they also have a large scalar sector
which may include stuff which isn't constrained by 4d gauge symmetry.
Any further questions?
You definately gave me some food for thought, thanks. I realize what I
was mostly wondering is if there were valid models of vector boson
exchange that don't have a guage symmetry. I'm not worried so much by
whether or not the interaction is renormalizable. Like I said, this is
pretty much just idle musing on my part: curiosity as to how much freedom
in phenomenologic models to fit the data that will come out of LHC we have
other than the same ol' theories defined almost entirely but what gauge
group you choose.
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| User: "Thomas Dent" |
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| Title: Re: Stupid questions |
04 Jul 2004 07:39:48 AM |
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Creighton Hogg <wchogg@hep.wisc.edu> wrote
Why don't you ask one of the many particle theory professors at
Wisconsin? They don't bite. (At least, not all of them.)
Yeah, I like all of the people I've met from the 5th floor. It's not
really a question for work, just my own idle musings, so I'd feel pretty
rude bugging them.
Well, if you can put together an informed, concise question, it won't
constitute bugging.
It's certainly not true that you are *only* allowed gauge
interactions. Perhaps you are misremembering the QFT class. If you
have only fermions and vectors and restrict yourself to renormalizable
theories, then this is the case. (That is, if you don't count fermion
mass terms as 'interactions'.)
(...)
I realize what I was mostly wondering is if there were valid models of
vector boson exchange that don't have a gauge symmetry. I'm not worried
so much by whether or not the interaction is renormalizable. Like I said,
this is pretty much just idle musing on my part: curiosity as to how much
freedom in phenomenologic models to fit the data that will come out of LHC
we have other than the same ol' theories defined almost entirely but what
gauge group you choose.
So, if you are interested specifically in theories of vectors, that
narrows it down quite a lot. There is a theorem somewhere saying that
if you require certain properties such as unitarity, renormalizability
etc. the only consistent theory (in Minkowski space) with vectors is
Yang-Mills. Unfortunately I can't remember the exact conditions to
prove the theorem. No doubt some prof. would know.
The fact that rho mesons, for example, exist, shows that vectors need
not be gauge bosons. Nuclear theory sometimes involves a sort of
phenomenological model of nucleon-nucleon forces involving (scalar
and) vector exchange which isn't gauge theory. But it's not a very
nice model because the cutoff is very low above which you lose
unitarity...
If you are thinking of the W and Z, there is of course the LEP
precision data that places very severe limits on what they can be.
From this they look pretty darn identical to gauge bosons.
Compositeness is ruled out up to quite high scales for example.
Incidentally you will find sci.physics.research a lot more convenient
for this sort of question than sci.physics.
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| User: "" |
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| Title: Re: Stupid questions |
02 Jul 2004 07:03:44 AM |
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[spit--off topic and will be rejected]
In article <cb504c2c.0407020304.c2f6ad3@posting.google.com>,
(Thomas Dent) wrote:
Creighton Hogg <wchogg@hep.wisc.edu> wrote
Are there other valid frameworks for describing forces, at energy levels
~10TeV or lower, besides gauge interactions (I'm including string theory
here because at low energy the contact interactions of strings have to
look like gauge interactions)? I seem to remember being
told in a QFT class that you're not allowed to have any other kinds of
interactions, but I honestly don't understand why. I'm just wondering
if
there's other options or if, at sufficiently low energy, everything
*must*
look a QFT with gauge interactions.
Why don't you ask one of the many particle theory professors at
Wisconsin? They don't bite. (At least, not all of them.)
I would always ask the ones who had reputation of biting. Those
who bite are the ones who have the answer plus a lot more.
<snip>
/BAH
Subtract a hundred and four for e-mail.
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| User: "Gregory L. Hansen" |
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| Title: Re: Stupid questions |
01 Jul 2004 08:07:16 PM |
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In article <Pine.LNX.4.44.0407011719310.13922-100000@azalea.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
This is one of those things that's occurred to me while waiting for
software to finish compiling.
Are there other valid frameworks for describing forces, at energy levels
~10TeV or lower, besides gauge interactions (I'm including string theory
here because at low energy the contact interactions of strings have to
look like gauge interactions)? I seem to remember being
told in a QFT class that you're not allowed to have any other kinds of
interactions, but I honestly don't understand why. I'm just wondering if
there's other options or if, at sufficiently low energy, everything *must*
look a QFT with gauge interactions.
Yep, that's a really stupid question there. I wish I knew the answer.
Seems to me you could write out whatever particle currents and
current-current interactions take your fancy. And if they don't fall into
a gauge symmetry, so what? Maybe the groups are important to maintain
logical consistency somewhere.
--
"Usenet is like a herd of performing elephants with diarrhea -- massive,
difficult to redirect, awe-inspiring, entertaining, and a source of
mind-boggling amounts of excrement when you least expect it. "
-- Gene Spafford, 1992
.
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| User: "Creighton Hogg" |
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| Title: Re: Stupid questions |
01 Jul 2004 09:15:20 PM |
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On Fri, 2 Jul 2004, Gregory L. Hansen wrote:
In article <Pine.LNX.4.44.0407011719310.13922-100000@azalea.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
This is one of those things that's occurred to me while waiting for
software to finish compiling.
Are there other valid frameworks for describing forces, at energy levels
~10TeV or lower, besides gauge interactions (I'm including string theory
here because at low energy the contact interactions of strings have to
look like gauge interactions)? I seem to remember being
told in a QFT class that you're not allowed to have any other kinds of
interactions, but I honestly don't understand why. I'm just wondering if
there's other options or if, at sufficiently low energy, everything *must*
look a QFT with gauge interactions.
Yep, that's a really stupid question there. I wish I knew the answer.
Seems to me you could write out whatever particle currents and
current-current interactions take your fancy. And if they don't fall into
a gauge symmetry, so what? Maybe the groups are important to maintain
logical consistency somewhere.
Well, within the context of QFT I *think* gauge symmetry is equivalent to
local charge conservation. My guess is that people would be loathe to
give up local charge conservation in favor of global because it seems
unrealistic, and I think it would also really screw with your allowed
interactions. If charge doesn't have to be conserved at the vertices of
your interaction, but rather just somewhere in the universe.
--
"Usenet is like a herd of performing elephants with diarrhea -- massive,
difficult to redirect, awe-inspiring, entertaining, and a source of
mind-boggling amounts of excrement when you least expect it. "
-- Gene Spafford, 1992
I swear you're the king of signatures, or at least in the royal family.
.
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| User: "Gregory L. Hansen" |
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| Title: Re: Stupid questions |
02 Jul 2004 08:26:00 AM |
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In article <Pine.LNX.4.44.0407012101250.24465-100000@azalea.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
On Fri, 2 Jul 2004, Gregory L. Hansen wrote:
In article <Pine.LNX.4.44.0407011719310.13922-100000@azalea.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
This is one of those things that's occurred to me while waiting for
software to finish compiling.
Are there other valid frameworks for describing forces, at energy levels
~10TeV or lower, besides gauge interactions (I'm including string theory
here because at low energy the contact interactions of strings have to
look like gauge interactions)? I seem to remember being
told in a QFT class that you're not allowed to have any other kinds of
interactions, but I honestly don't understand why. I'm just wondering if
there's other options or if, at sufficiently low energy, everything *must*
look a QFT with gauge interactions.
Yep, that's a really stupid question there. I wish I knew the answer.
Seems to me you could write out whatever particle currents and
current-current interactions take your fancy. And if they don't fall into
a gauge symmetry, so what? Maybe the groups are important to maintain
logical consistency somewhere.
Well, within the context of QFT I *think* gauge symmetry is equivalent to
local charge conservation. My guess is that people would be loathe to
give up local charge conservation in favor of global because it seems
unrealistic, and I think it would also really screw with your allowed
interactions. If charge doesn't have to be conserved at the vertices of
your interaction, but rather just somewhere in the universe.
I'm not sure off-hand how to prove that. But I think it is a more
productive direction to list the things we want from a theory, and see
what violence is done if we're not gauge symmetric.
I don't think we need local conservation of charge a priori, but that does
seem to be how the universe works.
Proca has, as far as I know, a perfectly good theory of massive light.
Greiner, in his book on field quantization, shows how to quantize it.
Massive light doesn't enjoy the same gauge symmetry as Maxwell's theory,
the potential no longer has an arbitrary zero. But I'm pretty sure charge
is still conserved. Maybe it has a different symmetry.
--
"Usenet is like a herd of performing elephants with diarrhea -- massive,
difficult to redirect, awe-inspiring, entertaining, and a source of
mind-boggling amounts of excrement when you least expect it. "
-- Gene Spafford, 1992
I swear you're the king of signatures, or at least in the royal family.
Thanks!
--
"There's nary an animal alive that can outrun a greased Scottsman!" --
Groundskeeper Willy
.
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| User: "Creighton Hogg" |
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| Title: Re: Stupid questions |
02 Jul 2004 10:23:14 AM |
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On Fri, 2 Jul 2004, Gregory L. Hansen wrote:
In article <Pine.LNX.4.44.0407012101250.24465-100000@azalea.hep.wisc.edu>,
Creighton Hogg <wchogg@hep.wisc.edu> wrote:
Well, within the context of QFT I *think* gauge symmetry is equivalent to
local charge conservation. My guess is that people would be loathe to
give up local charge conservation in favor of global because it seems
unrealistic, and I think it would also really screw with your allowed
interactions. If charge doesn't have to be conserved at the vertices of
your interaction, but rather just somewhere in the universe.
I'm not sure off-hand how to prove that. But I think it is a more
productive direction to list the things we want from a theory, and see
what violence is done if we're not gauge symmetric.
I don't think we need local conservation of charge a priori, but that does
seem to be how the universe works.
That's pretty much how it seems to me as well. There's no reason why you
*have* to have local instead of global conservation, but that is how all
forces we know of work. I still think though that it simplifies the
allowed interactions because you have to conserve charges at the vertices
of a feynman diagram rather than allowing correllated processes at
arbitrary distances that conserve charge when combined.
Proca has, as far as I know, a perfectly good theory of massive light.
Greiner, in his book on field quantization, shows how to quantize it.
Massive light doesn't enjoy the same gauge symmetry as Maxwell's theory,
the potential no longer has an arbitrary zero. But I'm pretty sure charge
is still conserved. Maybe it has a different symmetry.
Y'know, I have this book somewhere. I'll look that part up, because
you're right I don't seem to remember charge conservation getting screwed
up in the Proca theory.
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| User: "Timo Nieminen" |
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| Title: Re: Stupid questions |
01 Jul 2004 10:07:07 PM |
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On Thu, 1 Jul 2004, Creighton Hogg wrote:
On Fri, 2 Jul 2004, Gregory L. Hansen wrote:
"Usenet is like a herd of performing elephants with diarrhea -- massive,
difficult to redirect, awe-inspiring, entertaining, and a source of
mind-boggling amounts of excrement when you least expect it. "
-- Gene Spafford, 1992
I swear you're the king of signatures, or at least in the royal family.
Speaking of which, from what translation are your biblical sigs taken
from?
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "Gregory L. Hansen" |
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| Title: Re: Stupid questions |
02 Jul 2004 08:20:36 AM |
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In article <Pine.LNX.4.50.0407021305210.30152-100000@localhost>,
Timo Nieminen <timo@physics.uq.edu.au> wrote:
On Thu, 1 Jul 2004, Creighton Hogg wrote:
On Fri, 2 Jul 2004, Gregory L. Hansen wrote:
"Usenet is like a herd of performing elephants with diarrhea -- massive,
difficult to redirect, awe-inspiring, entertaining, and a source of
mind-boggling amounts of excrement when you least expect it. "
-- Gene Spafford, 1992
I swear you're the king of signatures, or at least in the royal family.
Speaking of which, from what translation are your biblical sigs taken
from?
I have a New American Bible. It's Catholic. I understand it doesn't
always synch with King James.
--
"There's nary an animal alive that can outrun a greased Scottsman!" --
Groundskeeper Willy
.
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