English

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