2005/09/30 by Dirk Kreimer · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Cohomology #Gauge (firearms) #Gauge fixing #Gauge theory #Homotopy and Cohomology in Algebraic Topology #Introduction to gauge theory #Quantum #Quantum field theory #Quantum gauge theory #Relationship between string theory and quantum field theory #Topological quantum field theory #hep-th #math.QA
paper · pdf · doi:10.1016/j.aop.2006.01.004
published as AnnalsPhys.321:2757-2781,2006 · 25p, uses feynmf, typos corrected, references added, to appear in Annals of Physics
arxiv created 2006/02/08 · openalex publication_date 2006/03/10 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.