QUANTUM GROUP GAUGE-THEORY ON CLASSICAL SPACES

We study the quantum group gauge theory developed elsewhere in the limit when the base space (spacetime) is a classical space rather than a general quantum space. We show that this limit of the theory for gauge quantum group U(q)(g) is isomorphic to usual gauge theory with Lie algebra g. Our analysis also illuminates certain inconsistencies in previous work on this topic where a different conclusion had been reached. In particular, we show that the use of the quantum trace in defining a Yang-Mills action in this setting as claimed by K. Wu and R.-J. Zhang [Commun. Theor. Phys. 17 (1992) 175] and by A.P. Isaev and Z. Popowicz [Phys. Lett. B 281 (1992) 2711 is not appropriate.