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Arithmetic and Geometry Around Quantization pp 277–292Cite as

Multiplicative Renormalization and Hopf Algebras

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Part of the book series: Progress in Mathematics ((PM,volume 279))

Summary

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.

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References

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Author information

Authors and Affiliations

  1. Institute for Mathematics, Astrophysics and Particle Physics Faculty of Science, Radboud Universiteit Nijmegen, Heyendaalseweg 135, Nijmegen, ED, 6525, The Netherlands

    Walter D. van Suijlekom

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

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Editors and Affiliations

  1. MPI für Mathematik, Vivatsgasse 7, Bonn, 53111, Germany

    Özgür Ceyhan  & Yu. I. Manin  & 

  2. Department of Mathematics, California Institute of Technology, 1200 E . California Blvd., Pasadena, CA, 91125, USA

    Matilde Marcolli

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van Suijlekom, W.D. (2010). Multiplicative Renormalization and Hopf Algebras. In: Ceyhan, Ö., Manin, Y.I., Marcolli, M. (eds) Arithmetic and Geometry Around Quantization. Progress in Mathematics, vol 279. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4831-2_10

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