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Quantization of singular systems and incomplete motions

N. P. Landsman
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Abstract

The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced representations of C*-algebras, in the light of L. Schwartz' theory of Hilbert subspaces. This turns out to account for the freedom in the induction procedure, at the same time providing a basis for generalized eigenfunction expansions pertinent to the needs of quantum cosmology. Reinforcing our previous proposal for the wave-function of the Universe, we are now able to add a concrete prescription for its calculation.

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N. P. Landsman. 1998-07-24. Quantization of singular systems and incomplete motions. https://arxiv.org/abs/gr-qc/9807069

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