Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
Abstract
Quantization of diffeomorphism invariant theories of connections is studied. A solutions of the diffeomorphism constraints is found. The space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions. This provides, in particular, a quantization of the Husain-Kuchař model. The main results also pave way to quantization of other diffeomorphism invariant theories such as general relativity. In the Riemannian case (i.e., signature ++++), the approach appears to contain all the necessary ingredients already. In the Lorentzian case, it will have to combined in an appropriate fashion with a coherent state transform to incorporate complex connections.
- Publication:
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Journal of Mathematical Physics
- Pub Date:
- November 1995
- DOI:
- 10.1063/1.531252
- arXiv:
- arXiv:gr-qc/9504018
- Bibcode:
- 1995JMP....36.6456A
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 30 pages Revtex, Section 6 corrected, references added, format changed