Planar Spin Network Coherent States II. Matrix Elements

Details Planar Spin Network Coherent States II. Matrix Elements Planar Spin Network Coherent States II. Matrix Elements

2008-07-07

arxiv.org/abs/0807.1035v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

58 pages

Scientific paper

This paper is the second of a series of three which construct coherent states for spin networks with planar symmetry. Paper 1 proposes a candidate set of coherent states. The present paper demonstrates explicitly that these states are approximate eigenvectors of the holonomy and momentum operators (as expected for coherent states), up to small correction terms. Those correction terms are calculated. A complete subset of the overcomplete set of coherent states is constructed, and used to compute the approximate inverse of the volume operator. A theorem of Thiemann and Winkler is used to calculate the matrix elements of the [volume, holonomy] commutator. In the classical limit this commutator takes the derivative of volume with respect to angular momentum L.

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