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Renormalization of Gauge Fields: A Hopf Algebra Approach

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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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  1. Walter D. van Suijlekom

    Present address: Institute for Mathematics, Astrophysics and Particle Physics, Radboud Universiteit, Toernooiveld 1, 6525 ED, Nijmegen, The Netherlands

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  1. Max Planck Institute for Mathematics, Vivatsgasse 7, D-53111, Bonn, Germany

    Walter D. van Suijlekom

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  1. Walter D. van Suijlekom
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Correspondence to Walter D. van Suijlekom.

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Communicated by A. Connes

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van Suijlekom, W.D. Renormalization of Gauge Fields: A Hopf Algebra Approach. Commun. Math. Phys. 276, 773–798 (2007). https://doi.org/10.1007/s00220-007-0353-9

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  • DOI: https://doi.org/10.1007/s00220-007-0353-9

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