Topological Graph Polynomials and Quantum Field Theory, Part I: Heat Kernel Theories

Details Topological Graph Polynomials and Quantum Field Theory, Part I: Heat Kernel Theories Topological Graph Polynomials and Quantum Field Theory, Part I: Heat Kernel Theories

2008-11-03

arxiv.org/abs/0811.0186v1

J.Noncommut.Geom.4:29-82,2010

Physics

Mathematical Physics

61 pages, 12 figures

Scientific paper

We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first paper we consider translation invariant theories with the usual heat-kernel-based propagator. We show how the Symanzik polynomials of quantum field theory are particular multivariate versions of the Tutte polynomial, and how the new polynomials of noncommutative quantum field theory are particular versions of the Bollob\'as-Riordan polynomials.

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