Scattering theory of space-time non-commutative abelian gauge field theory

TL;DR

This paper develops a scattering theory for space-time non-commutative QED, constructing a unitary S-matrix with a novel time ordering, and verifies gauge invariance at lowest order.

Contribution

It introduces a $ au$-time ordering for non-commutative QED, formulates perturbation theory, and explicitly checks gauge invariance in the non-commutative setting.

Findings

Constructed a unitary S-matrix for space-time non-commutative QED.

Presented Feynman rules for perturbation theory in this framework.

Verified gauge invariance at lowest order through Compton scattering.

Abstract

The unitary S-matrix for the space-time non-commutative QED is constructed using the $\star$-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, perturbation theory is formulated and Feynman rule is presented. The gauge invariance is explicitly checked to the lowest order, using the Compton scattering process. The gauge fixing condition dependency of the classical solution of the vacuum is also discussed.