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Title: The algebras of large N matrix mechanics

Abstract

Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

Authors:
;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Director. Office of Energy Research. Office of Basic Energy Sciences; National Science Foundation Grant PHY-95-14797 (US)
OSTI Identifier:
836360
Report Number(s):
LBNL-42212
R&D Project: PTHOPS; TRN: US0500565
DOE Contract Number:  
AC03-76SF00098
Resource Type:
Journal Article
Journal Name:
Inaternational Journal of Modern Physics A
Additional Journal Information:
Journal Volume: 14; Journal Issue: 19; Other Information: Submitted to International Journal of Modern Physics A: Volume 14, No.19; Journal Publication Date: 07/30/1999; PBD: 16 Sep 1999
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; HAMILTONIANS; SUPERSYMMETRY; LAWRENCE BERKELEY LABORATORY

Citation Formats

Halpern, M.B., and Schwartz, C. The algebras of large N matrix mechanics. United States: N. p., 1999. Web. doi:10.1142/S0217751X99001482.
Halpern, M.B., & Schwartz, C. The algebras of large N matrix mechanics. United States. doi:10.1142/S0217751X99001482.
Halpern, M.B., and Schwartz, C. Thu . "The algebras of large N matrix mechanics". United States. doi:10.1142/S0217751X99001482. https://www.osti.gov/servlets/purl/836360.
@article{osti_836360,
title = {The algebras of large N matrix mechanics},
author = {Halpern, M.B. and Schwartz, C.},
abstractNote = {Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.},
doi = {10.1142/S0217751X99001482},
journal = {Inaternational Journal of Modern Physics A},
number = 19,
volume = 14,
place = {United States},
year = {1999},
month = {9}
}