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Title: Anatomy of a gauge theory

Abstract

We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson-Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov-Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.

Authors:
 [1]
  1. IHES, 35 rte. de Chartres, 91440 Bures-sur-Yvette (France). E-mail: kreimer@ihes.fr
Publication Date:
OSTI Identifier:
20845946
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 321; Journal Issue: 12; Other Information: DOI: 10.1016/j.aop.2006.01.004; PII: S0003-4916(06)00024-8; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGEBRA; DYSON REPRESENTATION; EQUATIONS OF MOTION; GAUGE INVARIANCE; LIE GROUPS; QUANTUM FIELD THEORY

Citation Formats

Kreimer, Dirk. Anatomy of a gauge theory. United States: N. p., 2006. Web. doi:10.1016/j.aop.2006.01.004.
Kreimer, Dirk. Anatomy of a gauge theory. United States. doi:10.1016/j.aop.2006.01.004.
Kreimer, Dirk. Fri . "Anatomy of a gauge theory". United States. doi:10.1016/j.aop.2006.01.004.
@article{osti_20845946,
title = {Anatomy of a gauge theory},
author = {Kreimer, Dirk},
abstractNote = {We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson-Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov-Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams.},
doi = {10.1016/j.aop.2006.01.004},
journal = {Annals of Physics (New York)},
number = 12,
volume = 321,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}