Worldline approach to noncommutative field theory

TL;DR

This paper develops a worldline phase space approach to analyze heat-trace expansions in noncommutative field theories, providing a master formula that could address open problems like UV/IR mixing and nonlocal operators.

Contribution

It introduces a novel worldline method in phase space for noncommutative field theories, deriving a master formula for heat-trace expansions.

Findings

Derived a master formula for n-point heat-trace contributions.

Potential applications to noncommutative torus and renormalization.

Enhanced understanding of UV/IR mixing in noncommutative models.

Abstract

The study of the heat-trace expansion in noncommutative field theory has shown the existence of Moyal nonlocal Seeley-DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive to a master formula for the $n$-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the noncommutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other nonlocal operators.