Quantisation of -expanded non-commutative QEDJ.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 )
We analyse two new versions of -expanded non-commutative quantum electrodynamics up to first order in 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 . However, at higher order in the Seiberg-Witten map cannot be regarded as a field redefinition. We find that the initial action of any -expanded massless non-commutative QED must include one extra term proportional to which we identify by loop calculations.
© Società Italiana di Fisica, Springer-Verlag 2002