Non-linear Vacuum Phenomena in Non-commutative QED

TL;DR

This paper extends classic quantum electrodynamics results to non-commutative QED, revealing that non-perturbative effects are similar to commutative cases when viewed in a suitable frame, and showing that particles exhibit extended, dipolar-like behavior.

Contribution

It demonstrates the extension of Schwinger's results to non-commutative QED and uncovers the effective extended nature of particles in this framework.

Findings

Non-perturbative effects in constant backgrounds match commutative QED when using a related space-time frame.

Charged particles in non-commutative QED behave as 'half-dipoles', indicating an extended structure.

Evidence of retarded and advanced effects in scattering with plane wave backgrounds.

Abstract

We show that the classic results of Schwinger on the exact propagation of particles in the background of constant field-strengths and plane waves can be readily extended to the case of non-commutative QED. It is shown that non-perturbative effects on constant backgrounds are the same as their commutative counterparts, provided the on-shell gauge invariant dynamics is referred to a non-perturbatively related space-time frame. For the case of the plane wave background, we find evidence of the effective extended nature of non-commutative particles, producing retarded and advanced effects in scattering. Besides the known `dipolar' character of non-commutative neutral particles, we find that charged particles are also effectively extended, but they behave instead as `half-dipoles'.