Noncommutative Gauge Theory without Lorentz Violation

TL;DR

This paper develops a Lorentz-invariant noncommutative gauge theory by promoting the noncommutative parameter to an operator, resulting in a novel QED model with unique photon interactions.

Contribution

It introduces a Lorentz-preserving noncommutative algebra and constructs a corresponding gauge-invariant QED, avoiding Lorentz violation common in similar theories.

Findings

Lorentz invariance is maintained in the noncommutative framework.

Three-photon vertices are absent, but a four-photon coupling exists.

The theory predicts distinctive phenomenological signatures.

Abstract

The most popular noncommutative field theories are characterized by a matrix parameter theta^(mu,nu) that violates Lorentz invariance. We consider the simplest algebra in which the theta-parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology.