Violation of Remaining Lorentz Symmetry in the Approach of Time-Ordered Perturbation Theory to Space-Time Noncommutativity

TL;DR

This paper investigates how certain Lorentz symmetries are violated in time-ordered perturbation theory applied to space-time noncommutative theories, highlighting issues with phase factor transformations.

Contribution

It demonstrates the violation of remaining Lorentz symmetry in TOPT for space-time noncommutativity due to non-covariant phase factors.

Findings

Lorentz symmetry is violated in a simple scattering process.

Violation stems from non-covariant transformation of phase factors.

Remaining Lorentz transformations leave the noncommutativity parameter invariant.

Abstract

We study remaining Lorentz symmetry, i.e. Lorentz transformations which leave the noncommutativity parameter $\theta^{\mu\nu}$ invariant, within the approach of time-ordered perturbation theory (TOPT) to space-time noncommutative theories. Their violation is shown in a simple scattering process. We argue that this results from the non-covariant transformation properties of the phase factors appearing in TOPT.