The static effective action for non-commutative QED at high temperature

TL;DR

This paper derives the static effective action for non-commutative QED at high temperature, revealing $ heta$-dependent corrections to masses and gauge-invariant structures in the static limit.

Contribution

It provides a systematic derivation of the static effective action for non-commutative QED at high temperature, including $ heta$-dependent corrections and gauge-invariant formulations.

Findings

$ heta$-dependent corrections to electric and magnetic masses above a critical temperature

Closed form expression for the static gauge-invariant current

Validation of Ward identities in the static limit

Abstract

In this paper, we systematically study the effective action for non-commutative QED in the static limit at high temperature. When $\theta p^{2}\ll 1$, where $\theta$ represents the magnitude of the parameter for non-commutativity and $p$ denotes a typical external three momentum, we show that this leads naturally to a derivative expansion in this model. The study of the self-energy, in this limit, leads to nontrivial $\theta$ dependent corrections to the electric and magnetic masses, which exist only above a certain critical temperature. The three point and the four point amplitudes are also studied as well as their relations to the Ward identities in this limit. We determine the closed form expression for the current involving only the spatial components of the gauge field and present the corresponding static effective action, which is gauge invariant.