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

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arxiv gr-qc/9504018 v2 pith:TFFD2EAA submitted 1995-04-12 gr-qc

Abhay Ashtekar , Jerzy Lewandowski , Donald Marolf , Jose Mourao , Thomas Thiemann This is my paper · ORCID
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keywords diffeomorphismquantizationconnectionsinvarianttheoriescasesolutionsalready
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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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Cited by 5 Pith papers

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