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MP: Theoretische und Mathematische Grundlagen der Physik

MP 1: Quantenfeldtheorie und nichtkommutative Geometrie

MP 1.5: Fachvortrag

Montag, 15. März 2004, 15:40–16:05, H 22

Gauge Theory on Noncommutative Spaces: The q-deformed Euclidean Plane — •Frank Meyer — Max-Planck-Institut für Physik, Föhringer Ring 6, 80805 München, Germany

Gauge theory on the q-deformed two-dimensional Euclidean plane R_q² is studied using two different approaches. We first formulate the theory using the natural algebraic structures on R_q², such as a covariant differential calculus, a frame of one-forms and invariant integration. We then consider a suitable star product and introduce a natural way to implement the Seiberg-Witten map. In both approaches, gauge invariance requires a suitable “measure” in the action, breaking the E_q(2)-invariance. Some possibilities to avoid this conclusion using additional terms in the action are proposed.