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

Abhay Ashtekar·Jerzy Lewandowski·Donald Marolf·Jose Mourao·Thomas Thiemann
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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.

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Abhay Ashtekar, Jerzy Lewandowski, Donald Marolf, Jose Mourao, Thomas Thiemann. 1995-06-05. Quantization of diffeomorphism invariant theories of connections with local degrees of freedom. https://doi.org/10.1063/1.531252

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