Science > Physics > Quantum Algebra, Local Quantum Field Theory, Conformal Field Theory
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Science > Physics |
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"OsherD" |
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30 May 2005 01:53:48 AM |
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Quantum Algebra, Local Quantum Field Theory, Conformal Field Theory |
From Osher Doctorow
COPYRIGHT NOTICE
Quantum Algebra, Local Quantum Field Theory, Conformal Field Theory
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005
The word "local" usually means "in a small neighborhood of a point or
particle or (more recently) a little string or 0-brane".
Nonlocality in physics is more or less used for "action-at-a-distance"
or remote influences or even global influence over a large region
including many neighborhood ofs points etc.
I have been posting on locality vs nonlocality as they relate to PI
(Probable Influence) on math-history-list which is on Math Forum (type
keywords Math Forum and then select math-history-list from among their
free forums).
Einstein arguably began the notion of Locality in physics with his
General Relativity (GR) which locally can be said to reduce to either
Special Relativity (SR) or Classical Non-GR Physics.
Rudolf Haag of U. Hamburg is considered often to be the originator of
Local Quantum Field Theory (LQFT) in the last 35 years or so, and
depending on who categorizes them Quantum Algebra either began with
Wightman's version and shifted largely
to Haag's version or one distinguishes between the two schools.
Conformal Field Theory has become especially important recently in
physics via Superstring theory through Juan Maldacena and colleagues at
the Institute for Advanced Study and Harvard on AdS/CFT, that is to say
Anti-de-Sitter Space and Conformal Field Theory, although there have
been considerably many recent papers replacing AdS by dS (De Sitter
space) in certain contexts.
LQFT combines especially well with Conformal Field Theory (CFT), and
readers can find online papers and names of major researchers in LQFT
and LQP (Local Quantum Physics) via the keywords Local Quantum Physics
Crossorads, http://www.lqp.uni-goettingen.de. In fact, they abbreviate
their name LQP.
Probable Influence (PI) is, like LQP and LQFT and GR, oriented
toward Locality. In the case of PI, Probable Influence which
is P(A-->B) = P{(AB')'} = P(A' U B) = 1 + P(AB) - P(A) where
the probability of A, P(A), is less than .05 and AB is the
intersection of sets/events A, B (generalizable to processes).
There are some differences between PI and LQP and GR, but
Locality is one of the many similarities, and I'll try to
discuss these later.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Quantum Algebra, Local Quantum Field Theory, Conformal Field Theory |
30 May 2005 02:06:15 AM |
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From Osher Doctorow
Conformal Field Theory (CFT) is named after conformal transformations
which preserve angles but not necessarily lengths, and CFT is basically
2-dimensional.
Take a look at K.-H. Rehren (Inst. f. Theor. Physik U. Gottingen)
"Locality and modular invariance in 2D conformal QFT,"
arXiv:math-ph/0009004 v1 4 Sept 2000, as well as Bert Schroer's (CBPF
Brazil) "Two-dimensional models," hep-th/0502125 v3 26 Apr 2005, and Y.
Verbin's (The Open University of Israel, Tel Aviv) "Cosmic strings in
the Abelian Higgs model with conformal coupling to gravity,"
hep-th/9809002 v2 9 Feb 1999, the first two papers for LQP/CFT
relationships and the last for an interesting cosmological application
of the conformal framework.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Quantum Algebra, Local Quantum Field Theory, Conformal Field Theory |
30 May 2005 02:21:00 AM |
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From Osher Doctorow
Bert Schroer actually belongs to Institut fuer Theoretische Phsik der
FU Berlin, Germany, as well as CBPF in Brazil, and apparently comes
from Germany.
His 2005 paper is most interesting and is a contribution to
"Encyclopedia of Mathematical Physics". He is also a member of LQP
Crossroads. The paper is 28 pages, but well worth downloading (I used
Citation Index since arXiv somehow marked my computer for
"over-downloading papers"; anybody else who wants to use Citation Index
can usually find it below the arXiv listing of the paper). He uses 3
of the oldest models as examples: the Lenz-Ising model, Jordan's model
of bosonization/fermionization, and the QED_2 Schwinger model.
It's a bit late here, so I'll try to continue tomorrow.
Osher Doctorow
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