Anatomy of a gauge theory

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...

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Bibliographic Details
Published in:Annals of physics 2006-12, Vol.321 (12), p.2757-2781
Main Author: Kreimer, Dirk
Format: Article
Language:English
Subjects:
ALGEBRA
DYSON REPRESENTATION
EQUATIONS OF MOTION
GAUGE INVARIANCE
LIE GROUPS
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM FIELD THEORY
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Summary: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.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2006.01.004