General covariance, loops and matter

Details General covariance, loops and matter General covariance, loops and matter

1993-04-08

arxiv.org/abs/gr-qc/9304010v1

Phys.Rev. D47 (1993) 5394-5399

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

17 pages, Alberta-Thy-2-93 (RevTex)

Scientific paper

10.1103/PhysRevD.47.5394

A four dimensional generally covariant field theory is presented which describes non-dynamical three geometries coupled to scalar fields. The theory has an infinite number of physical observables (or constants of the motion) which are constructed from loops made from scalar field configurations. The Poisson algebra of these observables is closed and is the same as that for the 3+1 gravity loop variables in the Ashtekar formalism. The theory also has observables that give the areas of open surfaces and the volumes of finite regions. Solutions to all the Hamilton-Jacobi equations for the theory and the Dirac quantization conditions in the coordinate representation are given. These solutions are holonomies based on matter loops. A brief discussion of the loop space representation for the quantum theory is also given together with some implications for the quantization of 3+1 gravity.

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