Geometrodynamic Quantization and Time Evolution in Quantum Gravity

TL;DR

This paper introduces a novel quantization method for quantum gravity based on York's geometrodynamics, which separates dynamic variables from embedding parameters and provides a natural framework for time evolution.

Contribution

It presents a new geometrodynamic quantization procedure that explicitly distinguishes dynamic variables from embedding parameters, addressing the problem of time in quantum gravity.

Findings

Derives a linear Schrödinger equation with nonlinear classical constraints

Provides a self-consistent quantization approach for quantum geometrodynamics

Offers insights into the 'problems of time' in quantum gravity

Abstract

We advance here a new gravity quantization procedure that explicitly utilizes York's analysis of the geometrodynamic degrees of freedom. This geometrodynamic procedure of quantization is based on a separation of the true dynamic variables from the embedding parameters and a distinctly different treatment of these two kinds of variables. While the dynamic variables are quantized following the standard quantum mechanical and quantum field theoretic procedures, the embedding parameters are determined by the "classical" constraint equations in which the expectation values of the dynamic variables are substituted in place of their classical values. This self-consistent procedure of quantization leads to a linear Schrodinger equation augmented by nonlinear "classical" constraints and supplies a natural description of time evolution in quantum geometrodynamics. In particular, the procedure sheds new light on the "problems of time" in quantum gravity.