On the Operator Product Expansion in Noncommutative Quantum Field Theory

TL;DR

This paper investigates the operator product expansion in noncommutative quantum field theory, revealing limitations in describing field products via local operators due to IR/UV singularities and mixing effects.

Contribution

It provides a detailed analysis of the renormalization of local operators and demonstrates the failure of the standard OPE in noncommutative settings.

Findings

Identification of IR/UV singularities in local operators

Demonstration that field products cannot generally be expanded into local operators

Insights into UV/IR mixing effects in noncommutative QFT

Abstract

Motivated by the mixing of UV and IR effects, we test the OPE formula in noncommutative field theory. First we look at the renormalization of local composite operators, identifying some of their characteristic IR/UV singularities. Then we find that the product of two fields in general cannot be described by a series expansion of single local operator insertions.