Divergences in quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential

TL;DR

This paper investigates divergences in a noncommutative quantum field theory with Grosse-Wulkenhaar potential on two-dimensional Minkowski space, revealing a new divergence type that challenges model construction.

Contribution

It identifies a novel divergence in planar graphs at and above the self-dual point, impacting the feasibility of Minkowski space models.

Findings

Discovery of a new divergence in planar graphs

Divergence appears at and above the self-dual point

Potential obstruction to constructing Minkowski space Grosse-Wulkenhaar models

Abstract

Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position space. In both settings, we find a new type of divergence in planar graphs. It is present at and above the self-dual point. This new kind of divergence might make the construction of a Minkowski space version of the Grosse-Wulkenhaar model impossible.