English

Multiplicative renormalization and Hopf algebras

High Energy Physics - Theory 2007-07-05 v1

Abstract

We derive the existence of Hopf subalgebras generated by Green's functions in the Hopf algebra of Feynman graphs of a quantum field theory. This means that the coproduct closes on these Green's functions. It allows us for example to derive Dyson's formulas in quantum electrodynamics relating the renormalized and bare proper functions via the renormalization constants and the analogous formulas for non-abelian gauge theories. In the latter case, we observe the crucial role played by Slavnov--Taylor identities.

Keywords

Cite

@article{arxiv.0707.0555,
  title  = {Multiplicative renormalization and Hopf algebras},
  author = {Walter D. van Suijlekom},
  journal= {arXiv preprint arXiv:0707.0555},
  year   = {2007}
}

Comments

13 pages; uses feynmp

R2 v1 2026-06-21T08:54:59.448Z