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

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.

Expanded discussion of outlook for future research, in last three paragraphs. Corrected the typo in eq. (3). 12 pages

References in corpus (4)

• Quantum Spin Dynamics (QSD)
• Spherically Symmetric Quantum Geometry: States and Basic Operators
• Generating function techniques for loop quantum cosmology
• The volume operator for spin networks with planar or cylindrical symmetry

Cited by in corpus (6)

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• Hamiltonian dynamics of a quantum of space: hidden symmetries and spectrum of the volume operator, and discrete orthogonal polynomials
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• Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective
• Emergent modified gravity: Polarized Gowdy model on a torus