SU_q(n) Gauge Theory

Abstract

A field theory with local transformations belonging to the quantum group SU_q(n) is defined on a classical spacetime, with gauge potentials belonging to a quantum Lie algebra. Gauge transformations are defined for the potentials which lead to the appropriate quantum-group transformations for field strengths and covariant derivatives, defined for all elements of SU_q(n) by means of the adjoint action. This guarantees a non-trivial deformation. Gauge-invariant commutation relations are identified.Comment: 10 pages, Latex. The abstract and introduction have been hyped up to indicate more clearly what parts are refreshed by this quantum-group gauge theory that other quantum-group gauge theories cannot reach. To be published in Physics Letters