Zhituo Wang — Page 2

arXiv2008

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

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 Bollobás-Riordan polynomials.

math-ph↗

arXiv2007

Renormalization of Orientable Non-Commutative Complex $Φ^6_3$ Model

In this paper we prove that the Grosse-Wulkenhaar type non-commutative orientable complex scalar $ϕ^6_3$ theory, with two non-commutative coordinates and the third one commuting with the other two, is renormalizable to all orders in perturbation theory. Our proof relies on a multiscale analysis in x space.

hep-th↗