Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-12-23
Mod.Phys.Lett. A9 (1994) 2835-2848
Physics
High Energy Physics
High Energy Physics - Theory
7pp., plain TeX, DFTT-74/92
Scientific paper
Improving on an earlier proposal, we construct the gauge theories of the quantum groups $U_q(N)$. We find that these theories are consistent also with an ordinary (commuting) spacetime. 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 are given explicitly, and generalize the ordinary infinitesimal gauge variations. The $q$-lagrangian invariant under the $U_q(N)$ variations has the Yang-Mills form $\Fmn^i \Fmn^j g_{ij}$, the ``quantum metric'' $g_{ij}$ being a generalization of the Killing metric.
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