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Quantisation of θ-expanded non-commutative QED

Jesper M. Grimstrup·Raimar Wulkenhaar
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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.

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Jesper M. Grimstrup, Raimar Wulkenhaar. 2002-05-15. Quantisation of θ-expanded non-commutative QED. https://doi.org/10.1140/epjc%2Fs2002-01038-9

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