Combinatorial space from loop quantum gravity

Details Combinatorial space from loop quantum gravity Combinatorial space from loop quantum gravity

1997-03-14

arxiv.org/abs/gr-qc/9703038v2

Gen.Rel.Grav. 30 (1998) 1229-1245

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revised version. To be published in General Relativity and Gravitation, 14 pages, 1 figure

Scientific paper

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 respectably 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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