Intrinsic Time Deparameterization of The Canonical Connection Dynamics of General Relativity

TL;DR

This paper explores how intrinsic time deparameterization affects the phase space and dynamics of canonical gravity using Ashtekar variables, leading to a physical Hamiltonian and a classical master constraint formulation.

Contribution

It introduces a novel approach to incorporate intrinsic time into the connection formalism of canonical gravity, enabling a Hamiltonian evolution and complete observable construction.

Findings

Hamiltonian constraint becomes a physical Hamiltonian

Complete observables for the theory are constructed

Dynamics are formulated as a classical master constraint

Abstract

We investigate the implications of intrinsic time deparameterization on the phase space of the connection representation of canonical gravity in the form of the Ashtekar variables. We find that, much like the metric representation of this formalism, the Hamiltonian constraint now becomes a physical Hamiltonian generating evolution with respect to an intrinsic time. The complete observables for the theory are then constructed. Also, the dynamics in this formulation is cast into a classical master constraint theory.