  The metric for plane gravitational waves is quantized within the Hamiltonian
framework, using a Dirac constraint quantization and the self-dual field
variables proposed by Ashtekar. The z axis (direction of travel of the waves)
is taken to be the entire real line rather than the torus (manifold
coordinatized by (z,t) is RxR rather than $S_1$ x R). Solutions to the
constraints proposed in a previous paper involve open-ended flux lines running
along the entire z axis, rather than closed loops of flux; consequently, these
solutions are annihilated by the Gauss constraint at interior points of the z
axis, but not at the two boundary points. The solutions studied in the present
paper are based on closed flux loops and satisfy the Gauss constraint for all
z.
