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 nonlocal, relating states at two or more neighboring vertices.
- Received 7 December 2005
DOI:https://doi.org/10.1103/PhysRevD.73.124005
©2006 American Physical Society