DOI: 10.1140/epjc/s2002-01038-9
Quantisation of
-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
-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