Energy and directional signatures for plane quantized gravity waves

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.

54 pages; LaTex

References in corpus (3)

• Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity
• Total intrinsic spin for plane gravity waves
• Closed-Flux Solutions to the Constraints for Plane Gravity Waves

Cited by in corpus (7)

• Quantization of Midisuperspace Models
• Midi-superspace Models of Canonical Quantum Gravity
• Quantization of pure gravitational plane waves
• Towards Loop Quantization of Plane Gravitational Waves
• The volume operator for spin networks with planar or cylindrical symmetry
• Plane waves in quantum gravity: breakdown of the classical spacetime
• Quantum volume and length fluctuations in a midi-superspace model of Minkowski space