Topological graph polynomials and quantum field theory Part I: heat kernel theories | Zendy

Thomas Krajewski | Zendy; Vincent Rivasseau | Zendy; Adrian Tanasă | Zendy; Zhituo Wang | Zendy

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Topological graph polynomials and quantum field theory Part I: heat kernel theories

Author(s) -

Thomas Krajewski,

Vincent Rivasseau,

Adrian Tanasă,

Zhituo Wang

Publication year - 2010

Publication title -

journal of noncommutative geometry

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.037

H-Index - 26

eISSN - 1661-6960

pISSN - 1661-6952

DOI - 10.4171/jncg/49

Subject(s) - mathematics , topological quantum field theory , pure mathematics , discrete mathematics , topology (electrical circuits) , combinatorics

We investigate the relationship between the universal topological polynomialsfor graphs in mathematics and the parametric representation of Feynmanamplitudes in quantum field theory. In this first paper we consider translationinvariant theories with the usual heat-kernel-based propagator. We show how theSymanzik polynomials of quantum field theory are particular multivariateversions of the Tutte polynomial, and how the new polynomials of noncommutativequantum field theory are particular versions of the Bollob\'as-Riordanpolynomials.

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