Communications in Number Theory and Physics

Volume 2 (2008)

Number 4

Mixed Hodge structures and renormalization in physics

Pages: 637 – 718



Spencer Bloch (Department of Mathematics, University of Chicago)

Dirk Kreimer (Center for Mathematics and Physics, Boston University, Mass.)


This paper is a collaboration between a mathematician and a physicist. It is based on the observation that renormalization of Feynman amplitudes in physics is closely related to the theory of limiting mixed Hodge structures in mathematics. Whereas classical physical renormalization methods involve manipulations with the integrand of a divergent integral, limiting Hodge theory involves moving the chain of integration so the integral becomes convergent and studying the monodromy as the chain varies.

Published 1 January 2008