Translation-invariant models for non-commutative gauge fields

TL;DR

This paper introduces translation-invariant non-commutative U(1) gauge field models that incorporate additional terms to eliminate UV/IR mixing, inspired by recent scalar field models.

Contribution

It extends scalar field techniques to gauge fields, proposing new models that address UV/IR mixing in non-commutative gauge theories.

Findings

Models successfully incorporate extra terms to remove UV/IR mixing

Provides a framework for translation-invariant non-commutative gauge theories

Lays groundwork for further renormalization studies

Abstract

Motivated by the recent construction of a translation-invariant renormalizable non-commutative model for a scalar field (see arXiv:0802.0791 [math-ph]), we introduce models for non-commutative U(1) gauge fields along the same lines. More precisely, we include some extra terms into the action with the aim of getting rid of the UV/IR mixing.