Consistent Evolution with Different Time-Slicings in Quantum Gravity

TL;DR

This paper develops criteria for consistent, slicing-independent quantum evolution in quantum gravity, emphasizing a 'quantization after evolution' approach that aligns with classical limits, especially in (2+1)-dimensional models.

Contribution

It introduces criteria for slicing-independent quantum evolution in gravity, enabling a consistent 'quantization after evolution' framework compatible with classical limits.

Findings

Criteria for classical limit satisfaction are established.

Unitary evolution can be achieved across various time-slicings.

Applicability is demonstrated in (2+1)-dimensional gravity.

Abstract

Rovelli's `` quantum mechanics without time'' motivates an intrinsically time-slicing independent picture of reduced phase space quantum gravity, which may be described as ``quantization after evolution''. Sufficient criteria for carrying out quantization after evolution are developed in terms of a general concept of the classical limit of quantum mechanics. If these criteria are satisfied then it is possible to have consistent unitary evolution of operators, with respect to an infinite parameter family of time-slicings (and probably all time-slicings), with the correct classical limit. The criteria are particularly amenable to study in (2+1)-dimensional gravity, where the reduced phase space is finite dimensional.