General structure of the photon self-energy in non-commutative QED

TL;DR

This paper investigates the photon self-energy in non-commutative QED, demonstrating its transversality, renormalizability, and gauge independence of propagator poles across all orders and dimensions.

Contribution

It provides a comprehensive all-orders analysis of the photon self-energy in non-commutative QED, establishing transversality, renormalizability, and gauge independence.

Findings

Photon self-energy is transverse to all orders.

The theory is renormalizable using extended dimensional regularization.

Photon propagator poles are gauge independent.

Abstract

We study the behavior of the photon two point function, in non-commutative QED, in a general covariant gauge and in arbitrary space-time dimensions. We show, to all orders, that the photon self-energy is transverse. Using an appropriate extension of the dimensional regularization method, we evaluate the one-loop corrections, which show that the theory is renormalizable. We also prove, to all orders, that the poles of the photon propagator are gauge independent and briefly discuss some other related aspects.