Rota-Baxter Algebras in Renormalization of Perturbative Quantum Field Theory
Kurusch Ebrahimi-Fard, Li Guo
TL;DR
This paper explores the role of Rota-Baxter algebras in the renormalization process of perturbative quantum field theory, highlighting their mathematical structure and applications.
Contribution
It reviews the application of Rota-Baxter algebras in quantum field theory renormalization and related mathematical areas, providing a comprehensive overview.
Findings
Rota-Baxter algebras underpin the algebraic structure of renormalization.
They connect to multiple-zeta-values and matrix differential equations.
The paper clarifies the mathematical framework of renormalization in QFT.
Abstract
Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. In this context the notion of Rota-Baxter algebras enters the scene. We review several aspects of Rota-Baxter algebras as they appear in other sectors also relevant to perturbative renormalization, for instance multiple-zeta-values and matrix differential equations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.