Hamiltonian formulation of teleparallel gravity

Abstract

The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.Comment: 13 pages, no figures, comments welcom

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“…Furthermore, the geometry of spacetime is assumed to be torsionless by employing the Levi-Civita connection, which is torsionless by definition. While this is the most popular formulation, there exists an alternative but mathematically equivalent formulation called teleparallel gravity [1,2,3], differing from general relativity only by a boundary term. In this formulation, one instead uses the Weitzenböck connection, which is flat by definition.…”

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