Closed formula for the matrix elements of the volume operator in canonical quantum gravity

Details Closed formula for the matrix elements of the volume operator in canonical quantum gravity Closed formula for the matrix elements of the volume operator in canonical quantum gravity

1996-06-29

arxiv.org/abs/gr-qc/9606091v1

J.Math.Phys. 39 (1998) 3347-3371

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, Latex

Scientific paper

10.1063/1.532259

We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization which is state dependent but we are forced to it in order to maintain diffeomorphism covariance and in that sense it is natural. We arrive naturally at the expression for the volume operator as defined by Ashtekar and Lewandowski up to a state independent factor.

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