Renormalization via deformation of star products
DOI:
https://doi.org/10.48165/gjs.2026.3106Keywords:
Topological Hopf algebra of renormalization, Deformation of star products, Combinatorial Dyson--Schwinger equations, Feynman graphonsAbstract
Search for non-perturbative extensions of deformation quantization is one of the most important fundamental challenges in mathematical physics and quantum theories. Applying infinite combinatorics for the construction of mathematical foundations of non-perturbative quantum field theory has already been considered and developed as an alternative practical methodology for the study of strongly coupled gauge field theories. The present article reports the impact of this new practical methodology to deformation quantization. It is shown that the topological enrichment of the Hopf algebra of renormalization leads us to generate a new family of star products which (i) encode the renormalization of combinatorial Dyson–Schwinger equations, and (ii) provide a new non-perturbative quantization program for a certain family of noncommutative algebras. Results of this study addresses a new interconnection between deformation quantization and mathematical foundations of gauge field theories in the context of the topological Hopf algebra of renormalization
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