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The volume operator for singly polarized gravity waves with planar or cylindrical symmetry

Donald E. Neville
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Abstract

A previous paper constructed a kinematic basis for spin networks with planar or cylindrical symmetry and arbitrary polarization. This paper imposes a constraint which limits the gravitational wave to a single polarization. The spectrum of the constraint contains a physically reasonable number of zero eigenvalues, and the zero eigenvectors can be constructed explicitly. Commutation of the constraint with the Hamiltonian is expected to lead to a further constraint. This new constraint is not investigated in this paper, but I argue it will be non-local, relating states at two or more neighboring vertices.

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Donald E. Neville. 2006-06-12. The volume operator for singly polarized gravity waves with planar or cylindrical symmetry. https://doi.org/10.1103/physrevd.73.124005

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