CONSTRAINED QUANTIZATION, GAUGE-FIXING AND THE GRIBOV AMBIGUITY

The role played by gauge fixing in the description of superselection sectors 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) signals the existence of inequivalent reductions to a physical quantum theory, and hence superselection sectors. This point of view is contrasted with the more traditional one that identifies superselection sectors with inequivalent quantisations. It is argued that emphasising the role of gauge fixing (along with the Gribov problem) will allow for a more direct extension of these ideas to quantum field theory and, in particular, gauge theories.