https://doi.org/10.1007/s100520100857
Non-commutative Lorentz symmetry and the origin of the Seiberg–Witten map
1
Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstrasse 8–10, 1040 Wien, Austria
2
Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria
3
Physikalisches Institut der Universität Bonn, Nussallee 12, 53115 Bonn, Germany
Corresponding authors: a bichl@hep.itp.tuwien.ac.at - b jesper@hep.itp.tuwien.ac.at - c grosse@doppler.thp.univie.ac.at - d kraus@th.physik.uni-bonn.de - e popp@hep.itp.tuwien.ac.at, - f mschweda@tph.tuwien.ac.at - g raimar@doppler.thp.univie.ac.at
Received:
6
November
2001
Published online:
5
April
2002
We show that the non-commutative Yang–Mills field forms an irreducible representation of the (undeformed) Lie algebra of rigid translations, rotations and dilatations. The non-commutative Yang–Mills action is invariant under combined conformal transformations of the Yang–Mills field and of the non-commutativity parameter θ. The Seiberg–Witten differential equation results from a covariant splitting of the combined conformal transformations and can be computed as the missing piece to complete a covariant conformal transformation to an invariance of the action.
© Società Italiana di Fisica, Springer-Verlag, 2002