Closure of Constraints for Plane Gravity Waves

TL;DR

This paper demonstrates how the constraint algebra for canonical quantum gravity can be closed in the context of highly symmetric plane gravitational waves by a specific lapse function renormalization, ensuring correct diffeomorphism generation.

Contribution

It introduces a simple lapse function renormalization that enables the closure of the constraint algebra for plane gravitational waves in canonical quantum gravity.

Findings

Constraint algebra closes with the new lapse renormalization.

The vector constraint correctly generates spatial diffeomorphisms.

A measure respecting reality conditions is constructed.

Abstract

The metric for gravitational plane waves has very high symmetry (two spacelike commuting Killing vectors). For this high symmetry, a simple renormalization of the lapse function is found which allows the constraint algebra for canonical quantum gravity to close; also, the vector constraint has the correct form to generate spatial diffeomorphisms. A measure is constructed which respects the reality conditions, but does not yet respect the invariances of the theory.