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Particles and Fields

Eur. Phys. J. C 21, 383-388 (2001)
DOI: 10.1007/s100520100731

Construction of non-Abelian gauge theories on noncommutative spaces

B. Jurco1, L. Möller1, 2, 3, S. Schraml1, 3, P. Schupp1 and J. Wess1, 2, 3

1  Sektion Physik, Universität München, Theresienstrasse 37, 80333 München, Germany
2  Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München, Germany
3  Humboldt-Universität zu Berlin, Institut für Physik, Invalidenstrasse 110, 10115 Berlin, Germany

(Received: 13 June 2001 / Published online: 19 July 2001 -© Springer-Verlag / Società Italiana di Fisica 2001 )

We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories.

© Società Italiana di Fisica, Springer-Verlag 2001