Anatomy of a gauge theory

By Dirk Kreimer. 2005

142 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/180229a78eee986d2ec6d2aaf24b24c98b93af08

Citations in the corpus

• Renormalized Quantum Yang-Mills Fields in Curved Spacetime (2007, unknown): “Modern presentations of this approach based on the Hopf-algebra structure behind renormalization in the BPHZ-approach [21, 22, 83] are [105,106].”