Mixed Hodge Structures and Renormalization in Physics

TL;DR

This paper explores the connection between renormalization in quantum field theory and the mathematical framework of mixed Hodge structures, providing a novel perspective on the mathematical underpinnings of physical renormalization processes.

Contribution

It introduces a new approach linking renormalization to mixed Hodge structures through parametric Feynman graph representations, bridging physics and advanced mathematics.

Findings

Establishes a formal relationship between renormalization and mixed Hodge structures.

Provides a mathematical framework for understanding renormalization via Hodge theory.

Suggests new avenues for applying algebraic geometry to quantum field theory.

Abstract

We relate renormalization in perturbative quantum field theory to the theory of limiting mixed Hodge structures using parametric representations of Feynman graphs.