Solving gauge invariant systems without gauge fixing: The physical projector in 0+1 dimensional theories

The projector onto gauge invariant physical states was recently constructed for arbitrary constrained systems. This approach, which does not require g auge fixing nor any additional degrees of freedom beyond the original ones- two characteristic features of all other available methods for quantising c onstrained dynamics-is put to work in the context of a general class of qua ntum mechanical gauge invariant systems. The cases of SO(2) and SO(3) gauge groups are considered specifically, and a comprehensive understanding of t he corresponding physical spectra is achieved in a straightforward manner, using only standard methods of coherent states and group theory which are d irectly amenable to generalisation to other Lie algebras. Results extend co nsiderably the few examples available in the literature from much more subt le and delicate analyses implying gauge fixing and the characterization of modular space. (C) 1999 Academic Press.