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Gauge theory on the q-deformed two-dimensional Euclidean plane R^2_q isstudied using two different approaches. We first formulate the theory using thenatural algebraic structures on R^2_q, such as a covariant differentialcalculus, a frame of one-forms and invariant integration. We then consider asuitable star product, and introduce a natural way to implement theSeiberg-Witten map. In both approaches, gauge invariance requires a suitable``measure'' in the action, breaking the E_q(2)-invariance. Some possibilitiesto avoid this conclusion using additional terms in the action are proposed.Comment: 28 pages. v2: minor changes, published versio

GAUGE FIELD THEORY ON THE Eq(2)-COVARIANT PLANE

GAUGE FIELD THEORY ON THE E_q(2)-COVARIANT PLANE