English

Topological graph polynomials and quantum field theory, Part II: Mehler kernel theories

Mathematical Physics 2010-01-12 v2 math.MP

Abstract

We define a new topological polynomial extending the Bollobas-Riordan one, which obeys a four-term reduction relation of the deletion/contraction type and has a natural behavior under partial duality. This allows to write down a completely explicit combinatorial evaluation of the polynomials, occurring in the parametric representation of the non-commutative Grosse-Wulkenhaar quantum field theory. An explicit solution of the parametric representation for commutative field theories based on the Mehler kernel is also provided.

Keywords

Cite

@article{arxiv.0912.5438,
  title  = {Topological graph polynomials and quantum field theory, Part II: Mehler kernel theories},
  author = {Thomas Krajewski and Vincent Rivasseau and Fabien Vignes-Tourneret},
  journal= {arXiv preprint arXiv:0912.5438},
  year   = {2010}
}

Comments

58 pages, 23 figures, correction in the references and addition of preprint numbers

R2 v1 2026-06-21T14:29:23.332Z