QED on the Groenewold Moyal Plane

TL;DR

This paper explores noncommutative quantum electrodynamics on the Groenewold-Moyal plane, analyzing how noncommutativity affects scattering cross-sections and the Pauli principle, revealing shifts in expected zero-crossings.

Contribution

It provides explicit calculations of scattering processes in noncommutative QED, demonstrating the dependence of cross-sections on the noncommutativity parameter theta^{} and energy, and shows how fundamental symmetries are affected.

Findings

Elastic scattering cross-section zero shifted due to noncommutativity

Cross-sections depend explicitly on theta^{}

Pauli principle effects are modified in noncommutative setting

Abstract

We investigate a version of noncommutative QED where the interaction term, although natural, breaks the spin-statistics connection. We calculate $e^- + e^- -> e^- + e^-$ and $\gamma + e^- -> \gamma + e^-$ cross-sections in the tree approximation and explicitly display their dependence on theta^{\mu \nu}. Remarkably the zero of the elastic $e^- + e^- -> e^- + e^-$ cross-section at 90-degrees in the center-of-mass system, which is due to Pauli principle, is shifted away as a function of theta^{\mu \nu} and energy.