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Paper detail

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

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.

preprint2010arXivOpen access
Thomas KrajewskiVincent RivasseauFabien Vignes-Tourneret
math-phmath.MP
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Thomas KrajewskiVincent RivasseauFabien Vignes-Tourneret

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