Uq(2) Yang-Mills theory

A Yang-Mills theory is presented using the U-q(2) quantum group. Unlike previous works, no assumptions are required - between the quantum gauge parameters and the quantum gauge fields (or curvature) - to get the quantum gauge variations of the different fields. Furthermore, an adequate definition of the quantum trace is presented. Such a definition leads to a quantum metric, which therefore allows us to construct a U-q(2) quantum Yang-Mills Lagrangian. The Weinberg angle theta is found in terms of this q metric to be tan 2 theta = 2g(12,21)/g21,21-g12,12.