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Topological graph polynomials and quantum field theory. I: Theory kernel theories. (English) Zbl 1186.81095

The elationship between universal polynomials of Tutte and Bollobas-Riordan type and the parametric representation of Feynman amplitudes in quantum field theory is investigated. Translation invariant theories with the usual heat-kernel-based propagator are considered. It is shown how the Symanzik polynomials of quantum field theory are particular multivariate versions of the Tutte polynomial and the new polynomials of noncommutative quantum field theory are special versions of the Bollobas-Riordan polynomials.

MSC:

81T18 Feynman diagrams
05C31 Graph polynomials
05C05 Trees
05C10 Planar graphs; geometric and topological aspects of graph theory
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