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Combinatorial Space from Loop Quantum Gravity

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Abstract

The canonical quantization of diffeomorphism invariant theories of connections in terms of loop variables is revisited. Such theories include general relativity described in terms of Ashtekar-Barbero variables and extension to Yang-Mills fields (with or without fermions) coupled to gravity. It is argued that the operators induced by classical diffeomorphism invariant or covariant functions are respectively invariant or covariant under a suitable completion of the diffeomorphism group. The canonical quantization in terms of loop variables described here, yields a representation of the algebra of observables in a separable Hilbert space. Furthermore, the resulting quantum theory is equivalent to a model for diffeomorphism invariant gauge theories which replaces space with a manifestly combinatorial object.

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Authors
  1. José A. Zapata
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Zapata, J.A. Combinatorial Space from Loop Quantum Gravity. General Relativity and Gravitation 30, 1229–1245 (1998). https://doi.org/10.1023/A:1026699012787

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