Canonical General Relativity: the Diffeomorphism constraints and Spatial Frame Transformations

TL;DR

This paper develops a Hamiltonian formalism for Einstein's general relativity using metric and vielbein as independent variables, revealing constraints that generate spatial frame transformations and unifying different approaches.

Contribution

It introduces a consistent variational principle and a Hamiltonian formalism that includes spatial frame transformation constraints, unifying metric and vielbein formulations of general relativity.

Findings

Hamiltonian formalism with primary first class constraints

Constraints generate spatial frame transformations

Reproduces known constraint algebra results

Abstract

Einstein's general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as constraints that generate spatial frame transformations---all appearing as primary, first class constraints on phase space. The formalism encompasses the standard coordinate frame and vielbein approaches to general relativity, and the constraint algebra derived herein reproduces known results in either limit.