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arXiv · hep-th/0610137

Renormalization of gauge fields: A Hopf algebra approach

Walter D. van Suijlekom
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Abstract

We study the Connes-Kreimer Hopf algebra of renormalization in the case of gauge theories. We show that the Ward identities and the Slavnov-Taylor identities (in the abelian and non-abelian case respectively) are compatible with the Hopf algebra structure, in that they generate a Hopf ideal. Consequently, the quotient Hopf algebra is well-defined and has those identities built in. This provides a purely combinatorial and rigorous proof of compatibility of the Slavnov-Taylor identities with renormalization.

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Walter D. van Suijlekom. 2006-10-12. Renormalization of gauge fields: A Hopf algebra approach. https://doi.org/10.1007/s00220-007-0353-9

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