Vertex Algebras and Renormalization

  • Nikolay M. NikolovEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 314)


The Operator Product Expansion (OPE) and Renormalization Group (RG) are two of the most advanced and sophisticated structures in Quantum Field Theory (QFT). With this work we aim to show that the complexity in those areas is contained in one and the same universal operad structure. In more detail, this is a symmetric operad (with derivations) and its universality means that it is model independent within a large class of QFT models. The latter operad we call expansion operad. In the context of renormalization theory we find an isomorphic operad, which we call renormalization operad. The applications of the latter are for the description of the so called renormalization group and its action on the space of physical coupling constants via formal diffeomorphisms.


Quantum Field Theory Vertex Algebras Operads Renormalization Group 



The author thanks for the useful discussions with Spencer Bloch, Francis Brown, Pierre Cartier and Maxim Kontsevich on various topics related to this work during his visits at Institut des Hautes Études Scientifiques (IHÉS, Bures-sur-Yvette, France). The author is grateful for the support and hospitality by Instituto de Ciencias Matemáticas (ICMAT, Madrid), where this work was presented during the Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory (ICMAT, September 15–December 19, 2014). The author thanks the referees for their careful reading of the manuscript an for suggesting many corrections and improvements. This work was supported in part by the Bulgarian National Science Fund under research grant DN-18/3.


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Authors and Affiliations

  1. 1.Institute for Nuclear Research and Nuclear Energy of Bulgarian Academy of SciencesSofiaBulgaria

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