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A Hopf algebra deformation approach to renormalization

Lucian M. Ionescu·Michael Marsalli
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Abstract

We investigate the relation between Connes-Kreimer Hopf algebra approach to renomalization and deformation quantization. Both approaches rely on factorization, the correspondence being established at the level of Wiener-Hopf algebras, and double Lie algebras/Lie bialgebras, via r-matrices. It is suggested that the QFTs obtained via deformation quantization and renormalization correspond to each other in the sense of Kontsevich/Cattaneo-Felder.

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Lucian M. Ionescu, Michael Marsalli. 2003-07-11. A Hopf algebra deformation approach to renormalization. https://arxiv.org/abs/hep-th/0307112

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