Quantisation of $\theta$-expanded non-commutative QED

J.M. Grimstrup; R. Wulkenhaar

doi:doi:10.1140/epjc/s2002-01038-9

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2022 Impact factor 4.4

Particles and Fields

Eur. Phys. J. C 26, 139-151 (2002)
DOI: 10.1140/epjc/s2002-01038-9

Quantisation of $\theta$ -expanded non-commutative QED

J.M. Grimstrup¹ and R. Wulkenhaar²

¹ Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstraße 8-10, 1040 Wien, Austria
² Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstraße 22-26, 04103 Leipzig, Germany

(Received: 3 July 2002 / Published online: 7 October 2002 )

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.