Quantisation of θ-expanded non-commutative QED

Abstract

We analyse two new versions of θ-expanded non-commutative quantum electrodynamics up to first order in θand 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 θ. However, at higher order in θthe Seiberg-Witten map cannot be regarded as a field redefinition. We find that the initial action of any θ-expanded massless non-commutative QED must include one extra term proportional to θwhich we identify by loop calculations.