REDUCTION, QUANTIZATION, AND NONUNIMODULAR GROUPS

It is shown that even in relatively nice cases the naive approach to the quantization of constraints is not correct in general [i.e., the procedure that if f = 0 is a classical constraint and τ(f) is the associated quantum operator, then the quantum constraint is τ(f) = 0]. An explicit procedure for the quantization of constraints in the case of a configuration space with a symmetry group is provided and proven, where the reduced configuration space is the orbit space. It is not thought that the group acts freely, merely that all isotropy subgroups are conjugated to each other. © 1969 American Institute of Physics.