Anatomy of a gauge theory

Journal Article · Fri Dec 15 04:00:00 EST 2006 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2006.01.004· OSTI ID:20845946

Kreimer, Dirk ^[1]

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1. IHES, 35 rte. de Chartres, 91440 Bures-sur-Yvette (France)

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.

• OSTI ID: 20845946
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 12 Vol. 321; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
DYSON REPRESENTATION
EQUATIONS OF MOTION
GAUGE INVARIANCE
LIE GROUPS
QUANTUM FIELD THEORY