Partition function methods for the quartic scalar quantum field theory on the Moyal plane

TL;DR

This paper explores partition function techniques for the quartic scalar quantum field theory on the Moyal plane, focusing on factorization methods and their limitations in weak coupling regimes.

Contribution

It introduces an asymptotic approach to polytope volume calculation and analyzes its impact on the matrix structure of the quantum field theory.

Findings

Polytope volume asymptotics are determined.

Factorization approach is applicable in weak coupling.

Asymptotic character causes fictitious divergences.

Abstract

In this work several techniques to treat the partition function of the real scalar quartic quantum field theory on the Moyal plane is discussed. A factorisation approach requires the polytope volume for the diagonal subpolytope of symmetric stochastic matrices. This is determined asymptotically. The applicability of this method is tested for regime of weak coupling. Here the asymptotic character of the polytope volume alters the matrix structure of the original model leading to fictitious divergences.