Weave states for plane gravitational waves

In the nonperturbative approach for quantizing gravity in terms of Ashtekar variables, the weave states, approximating given classical metrics at large scales, play an important role. In the present paper we construct the weave states for an exact solution of Einstein's equations, representing plane gravitational waves. We also investigate the low-energy limit for the exact and linearized cases and show that in the exact case no splitting into a background metric plus perturbation occurs. We discuss the "small" and "large-loop" weave states and comment on their applications.