Quantization of pure gravitational plane waves

TL;DR

This paper develops a quantum model of pure gravitational plane waves by reducing the classical phase space, analyzing its symplectic structure, and applying Fock quantization to the simplified system.

Contribution

It introduces a gauge-fixed, constraint-free reduced model for gravitational plane waves and quantizes it using a Fock representation, providing a new approach to quantum gravity in this context.

Findings

Reduced phase space described by creation and annihilation variables

Quantization achieved through Fock representation

Classical solutions correspond to plane waves with no constraints

Abstract

Pure gravitational plane waves are considered as a special case of spacetimes with two commuting spacelike Killing vector fields. Starting with a midisuperspace that describes this kind of spacetimes, we introduce gauge-fixing and symmetry conditions that remove all non-physical degrees of freedom and ensure that the classical solutions are plane waves. In this way, we arrive at a reduced model with no constraints and whose only degrees of freedom are given by two fields. In a suitable coordinate system, the reduced Hamiltonian that generates the time evolution of this model turns out to vanish, so that all relevant information is contained in the symplectic structure. We calculate this symplectic structure and particularize our discussion to the case of linearly polarized plane waves. The reduced phase space can then be described by an infinite set of annihilation and creation like variables. We finally quantize the linearly polarized model by introducing a Fock representation for these variables.