Quantization of diffeomorphism invariant theories of connections with local degrees of freedom

Details Quantization of diffeomorphism invariant theories of connections with local degrees of freedom Quantization of diffeomorphism invariant theories of connections with local degrees of freedom

1995-04-12

arxiv.org/abs/gr-qc/9504018v2

J.Math.Phys.36:6456-6493,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages Revtex, Section 6 corrected, references added, format changed

Scientific paper

10.1063/1.531252

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-Kucha\v{r} 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.

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