ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

Abstract

We present a new Hamiltonian formulation of the Teleparallel Equivalent of General Relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on a spacetime. The Hamiltonian formulation is derived by means of an ADM-like 3+1 decomposition of the field and without any gauge fixing. A complete set of constraints on the phase space and their algebra are presented. The formulation is described in terms of differential forms.

43 pages, LaTeX2e; the original 73 page paper arXiv:1111.5498v1 was revised and divided into two parts. The present paper is the first part of the original one (the second part is available as arXiv:1309.4685)

References in corpus (10)

• The teleparallel equivalent of general relativity
• Gravity quantized
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• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra
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Cited by in corpus (19)

• Teleparallel Gravity: From Theory to Cosmology
• Hamiltonian and primary constraints of new general relativity
• Review of the Hamiltonian analysis in teleparallel gravity
• Hamiltonian formulation of teleparallel gravity
• On the gauge fixing in the Hamiltonian analysis of general teleparallel theories
• Construction of spaces of kinematic quantum states for field theories via projective techniques
• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity I
• Teleparallel bigravity
• Hamiltonian of new general relativity using differential forms
• Hamiltonian Analysis In New General Relativity
• The generalization of the ADM gravitational energy-momentum
• The Hamiltonian constraint in the symmetric teleparallel equivalent of general relativity
• Constraints of the Teleparallel Equivalent of General Relativity in a gauge
• Space of quantum states built over metrics of fixed signature
• Gravitational energy in pp-wave spacetimes
• The Einstein constraints and differential forms