4 Ju n 20 08 A new approach to the quantization of totally constrained systems

A new approach to the quantization of totally constrained systems. Abstract In this paper we present a new approach to the quantization which uses the semiclassical-quantum (SQC) correspondence to deduce the form of the wavefunction of the universe corresponding to a general totally constrained system. The implementation of the constraints can be seen as the breaking of a translational symmetry in functional space of the unconstrained wavefunction, which is directly analogous to fixing a gauge in exchange for a convergent path integral as in nonabelian gauge theory. We derive the wavefunction of the universe by the canon-ical, geometric and path integration approaches for a general system satisfying the SQC, highlighting their equivalence. We also relate the original second-quantized system to a third quantized system, both of which are amenable to perturbative expansion to reveal its renormaliz-ability properties. Additionally, we also comment on the issue of time for totally constrained systems.