Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2005-09-17
AnnalsPhys.321:2757-2781,2006
Physics
High Energy Physics
High Energy Physics - Theory
25p, uses feynmf, typos corrected, references added, to appear in Annals of Physics
Scientific paper
10.1016/j.aop.2006.01.004
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.
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