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Title: Towards a loop representation of connection theories defined over a super Lie algebra

Abstract

The purpose of this contribution is to review some aspects of the loop space formulation of pure gauge theories having the connection defined over a Lie algebra. The emphasis is focused on the discussion of the Mandelstam identities, which provide the basic constraints upon both the classical and the quantum degrees of freedom of the theory. In the case where the connection is extended to be valued on a super Lie algebra, some new results are presented which can be considered as first steps towards the construction of the Mandelstam identities in this situation, which encompasses such interesting cases as supergravity in 3+1 dimensions together with 2+1 super Chern-Simons theories, for example. Also, these ideas could be useful in the loop space formulation of fully supersymmetric theories. {copyright} {ital 1996 American Institute of Physics.}

Authors:
 [1]
  1. Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, 09340 (Mexico), D. F.
Publication Date:
OSTI Identifier:
401038
Report Number(s):
CONF-9511225-
Journal ID: APCPCS; ISSN 0094-243X; TRN: 96:029237
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 359; Journal Issue: 1; Conference: Workshop on particles and fields and phenomenology of fundamental interactions, Puebla (Mexico), Nov 1995; Other Information: PBD: Feb 1996
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; GRADED LIE GROUPS; REVIEWS; UNIFIED-FIELD THEORIES; MANDELSTAM REPRESENTATION; WILSON LOOP; LAGRANGIAN FUNCTION; YANG-MILLS THEORY; HAMILTONIAN FUNCTION; SUPERSYMMETRY

Citation Formats

Urrutia, L F, and Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, 04510. Towards a loop representation of connection theories defined over a super Lie algebra. United States: N. p., 1996. Web. doi:10.1063/1.49736.
Urrutia, L F, & Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, 04510. Towards a loop representation of connection theories defined over a super Lie algebra. United States. https://doi.org/10.1063/1.49736
Urrutia, L F, and Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, 04510. 1996. "Towards a loop representation of connection theories defined over a super Lie algebra". United States. https://doi.org/10.1063/1.49736.
@article{osti_401038,
title = {Towards a loop representation of connection theories defined over a super Lie algebra},
author = {Urrutia, L F and Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, 04510},
abstractNote = {The purpose of this contribution is to review some aspects of the loop space formulation of pure gauge theories having the connection defined over a Lie algebra. The emphasis is focused on the discussion of the Mandelstam identities, which provide the basic constraints upon both the classical and the quantum degrees of freedom of the theory. In the case where the connection is extended to be valued on a super Lie algebra, some new results are presented which can be considered as first steps towards the construction of the Mandelstam identities in this situation, which encompasses such interesting cases as supergravity in 3+1 dimensions together with 2+1 super Chern-Simons theories, for example. Also, these ideas could be useful in the loop space formulation of fully supersymmetric theories. {copyright} {ital 1996 American Institute of Physics.}},
doi = {10.1063/1.49736},
url = {https://www.osti.gov/biblio/401038}, journal = {AIP Conference Proceedings},
number = 1,
volume = 359,
place = {United States},
year = {Thu Feb 01 00:00:00 EST 1996},
month = {Thu Feb 01 00:00:00 EST 1996}
}