Gauge-Invariant Resummation Formalism and Unitarity in Non-Commutative QED

TL;DR

This paper develops a gauge-invariant resummation approach for non-commutative QED, ensuring unitarity and analyzing IR/UV mixing effects, with implications for Schwinger-Dyson equations and photon mass generation.

Contribution

It extends pinch techniques to non-commutative QED, enabling gauge-invariant resummation and unitarity checks, and explores IR/UV mixing effects in two dimensions.

Findings

Pinched gluon self-energy is gauge-independent.

Resummed propagators lack unphysical thresholds.

Finite gauge-invariant photon mass contribution in 2D due to IR/UV mixing.

Abstract

We re-examine the perturbative properties of four-dimensional non-commutative QED by extending the pinch techniques to the theta-deformed case. The explicit independence of the pinched gluon self-energy from gauge-fixing parameters, and the absence of unphysical thresholds in the resummed propagators permits a complete check of the optical theorem for the off-shell two-point function. The known anomalous (tachyonic) dispersion relations are recovered within this framework, as well as their improved version in the (softly broken) SUSY case. These applications should be considered as a first step in constructing gauge-invariant truncations of the Schwinger-Dyson equations in the non-commutative case. An interesting result of our formalism appears when considering the theory in two dimensions: we observe a finite gauge-invariant contribution to the photon mass because of a novel incarnation of IR/UV mixing, which survives the commutative limit when matter is present.