Quantization of Singular Systems and Incomplete Motions
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.
- Publication:
-
Current Topics in Mathematical Cosmology
- Pub Date:
- 1998
- DOI:
- 10.48550/arXiv.gr-qc/9807069
- arXiv:
- arXiv:gr-qc/9807069
- Bibcode:
- 1998ctmc.conf..256L
- Keywords:
-
- General Relativity and Quantum Cosmology
- E-Print:
- 8 pages