Uq(N) GAUGE THEORIES
Improving on an earlier proposal, we construct the gauge theories of the quantum groups U q(N). We find that these theories are also consistent with an ordinary (commuting) space-time. The bicovariance conditions of the quantum differential calculus are essential in our construction. The gauge potentials and the field strengths are q-commuting "fields," and satisfy q-commutation relations with the gauge parameters. The transformation rules of the potentials generalize the ordinary infinitesimal gauge variations. For particular deformations of U (N) ("minimal deformations"), the algebra of quantum gauge variations is shown to close, provided the gauge parameters satisfy appropriate q-commutations. The q-Lagrangian invariant under the U q(N) variations has the Yang–Mills form [Formula: see text], the "quantum metric" gij being a generalization of the Killing metric.