Gauge theories on the -Minkowski spacetime
Fakultät für Physik, Universität München, Theresienstr. 37, 80333, München, Germany
2 Max-Planck-Institut für Physik, Föhringer Ring 6, 80805, München, Germany
3 Faculty of Physics, University of Belgrade, Studentski trg 12, 11000, Beograd, Serbia and Montenegro
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This study of gauge field theories on -deformed Minkowski spacetime extends previous work on field theories on this example of a non-commutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the concept of enveloping algebra-valued gauge transformations and the Seiberg-Witten formalism. Derivative-valued gauge fields lead to field strength tensors as the sum of curvature- and torsion-like terms. We construct the Lagrangians explicitly to first order in the deformation parameter. This is the first example of a gauge theory that possesses a deformed Lorentz covariance.
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