Probing quantized Einstein-Rosen waves with massless scalar matter

The purpose of this paper is to discuss in detail the use of scalar matter coupled to linearly polarized Einstein-Rosen waves as a probe to study quantum gravity in the restricted setting provided by this symmetry reduction of general relativity. We will obtain the relevant Hamiltonian and quantize it with the techniques already used for the purely gravitational case. Finally, we will discuss the use of particlelike modes of the quantized fields to operationally explore some of the features of quantum gravity within this framework. Specifically, we will study two-point functions, the Newton-Wigner propagator, and radial wave functions for one-particle states.