Invariant Hamiltonian Quantization of General Relativity

TL;DR

This paper develops a reparametrization-invariant Hamiltonian quantization of General Relativity, introducing an invariant evolution parameter and analyzing the resulting functional and physical implications.

Contribution

It constructs a new invariant Hamiltonian framework for quantizing GR that preserves reparametrization invariance, differing from traditional approaches.

Findings

Invariance of the quantization under time-reparametrizations.

Introduction of the zero Fourier harmonic as an evolution parameter.

Discussion of physical consequences in the infinite space-time limit.

Abstract

The quantization of General Relativity invariant with respect to time-reparametrizations is considered. We construct the Faddeev-Popov generating functional for the unitary perturbation theory in terms of invariants of the kinemetric group of diffeomorphisms of a frame of reference as a set of Einstein's observers with the equivalent Hamiltonian description ($t'=t'(t)$, $x'^i=x'^i(t,x^1,x^2,x^3)$). The algebra of the kinemetric group has other dimensions than the constraint algebra in the conventional Dirac-Faddeev-Popov (DFP) approach to quantization. To restore the reparametrization invariance broken in the DFP approach, the invariant dynamic evolution parameter is introduced as the zero Fourier harmonic of the space metric determinant. The unconstrained version of the reparametrization invariant GR is obtained. We research the infinite space-time limit of the Faddeev-Popov generating functional in the theory and discuss physical consequences of the considered quantization.