SUq(n) gauge theory

A field theory with local transformations belonging to the quantum group SUq(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 SUq(n) by means of the adjoint action. This guarantees a non-trivial deformation. Gauge-invariant commutation relations are identified.