Gauge Field Theory on the E_q(2)-covariant Plane

Details Gauge Field Theory on the E_q(2)-covariant Plane Gauge Field Theory on the E_q(2)-covariant Plane

2003-09-04

arxiv.org/abs/hep-th/0309053v2

Int.J.Mod.Phys. A19 (2004) 3349-3376

Physics

High Energy Physics

High Energy Physics - Theory

28 pages. v2: minor changes, published version

Scientific paper

10.1142/S0217751X04019512

Gauge theory on the q-deformed two-dimensional Euclidean plane R^2_q is studied using two different approaches. We first formulate the theory using the natural algebraic structures on R^2_q, 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.

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