The volume operator for spin networks with planar or cylindrical symmetry

Details The volume operator for spin networks with planar or cylindrical symmetry The volume operator for spin networks with planar or cylindrical symmetry

2005-11-01

arxiv.org/abs/gr-qc/0511005v2

Phys.Rev.D73:124004,2006; Erratum-ibid.D77:129901,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

35 pages

Scientific paper

10.1103/PhysRevD.73.124004

This paper constructs a kinematic basis for spin networks with planar or cylindrical symmetry, by exploiting the fact that the basis elements are representations of an O(3) subgroup of O(4). The action of the volume operator on this basis gives a difference equation for the eigenvalues and eigenvectors of the volume operator. For basis elements of low spin, the difference equation can be solved readily on a computer. For higher spins, I solve for the eigenvalues using a WKBJ method. This paper considers only the case where the gravitational wave can have both polarizations. The single polarization case is considered in a spearate paper.

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