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 F(munu)iF(munugij)j, the ''quantum metric'' g(ij) being a generalization of the Killing metric.