Quantisation of \theta-expanded non-commutative QED

TL;DR

This paper investigates two formulations of heta-expanded non-commutative QED at first order in heta and loop level, revealing the role of the Seiberg-Witten map and identifying necessary additional terms for consistency.

Contribution

It compares two versions of heta-expanded non-commutative QED and clarifies the limitations of the Seiberg-Witten map beyond first order, also identifying an extra term needed in the action.

Findings

Seiberg-Witten map acts as a field redefinition at first order in heta.

At higher order, the Seiberg-Witten map cannot be regarded as a simple field redefinition.

An extra heta-dependent term is required in the initial action for consistency.

Abstract

We analyse two new versions of \theta-expanded non-commutative quantum electrodynamics up to first order in \theta and first loop order. In the first version we expand the bosonic sector using the Seiberg-Witten map, leaving the fermions unexpanded. In the second version we leave both bosons and fermions unexpanded. The analysis shows that the Seiberg-Witten map is a field redefinition at first order in \theta. However, at higher order in \theta the Seiberg-Witten map cannot be regarded as a field redefinition. We find that the initial action of any \theta-expanded massless non-commutative QED must include one extra term proportional to \theta which we identify by loop calculations.