Energy and directional signatures for plane quantized gravity waves

TL;DR

This paper constructs solutions to quantum constraints in planar gravity using Ashtekar variables, introduces new directionality operators, and discusses the implications for quantum unidirectionality and area evolution.

Contribution

It introduces quantum operators sensitive to wave directionality and analyzes their relation to classical constraints, advancing the understanding of quantum plane gravitational waves.

Findings

Operators sensitive to wave directionality are constructed.

Quantum BPR constraints predict unidirectionality in semiclassical solutions.

A mechanism preventing quantum collapse of area is proposed.

Abstract

Solutions are constructed to the quantum constraints for planar gravity (fields dependent on z and t only) in the Ashtekar complex connection formalism. A number of operators are constructed and applied to the solutions. These include the familiar ADM energy and area operators, as well as new operators sensitive to directionality (z+ct vs. z-ct dependence). The directionality operators are quantum analogs of the classical constraints proposed for unidirectional plane waves by Bondi, Pirani, and Robinson (BPR). It is argued that the quantum BPR constraints will predict unidirectionality reliably only for solutions which are semiclassical in a certain sense. The ADM energy and area operators are likely to have imaginary eigenvalues, unless one either shifts to a real connection, or allows the connection to occur other than in a holonomy. In classical theory, the area can evolve to zero. A quantum mechanical mechanism is proposed which would prevent this collapse.