Anatomy of a gauge theory
High Energy Physics - Theory
2008-11-26 v3 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.hep-th/0509135,
title = {Anatomy of a gauge theory},
author = {Dirk Kreimer},
journal= {arXiv preprint arXiv:hep-th/0509135},
year = {2008}
}
Comments
25p, uses feynmf, typos corrected, references added, to appear in Annals of Physics