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.
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