CONSTRAINED QUANTIZATION, GAUGE-FIXING AND THE GRIBOV AMBIGUITY

The role played by gauge fixing in the description of superselection s ectors for a simple quantum mechanical system is analysed. By viewing this as a theory with constraints, it is shown that the possibility of having inequivalent gauge fixing conditions (Gribov's ambiguity) sign als the existence of inequivalent reductions to a physical quantum the ory, and hence superselection sectors. This point of view is contraste d with the more traditional one that identifies superselection sectors with inequivalent quantisations. It is argued that emphasising the ro le of gauge fixing (along with the Gribov problem) will allow for a mo re direct extension of these ideas to quantum field theory and, in par ticular, gauge theories.