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Canonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge

A. A. Sousa·J. W. Maluf
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Abstract

We consider the most general class of teleparallel gravitational {}{}theories quadratic in the torsion tensor, in three space-time dimensions, and carry out a detailed investigation of its Hamiltonian formulation in Schwinger's time gauge. This general class is given by a family of three-parameter theories. A consistent implementation of the Legendre transform reduces the original theory to a one-parameter family of theories. By calculating Poisson brackets we show explicitly that the constraints of the theory constitute a first-class set. Therefore the resulting theory is well defined with regard to time evolution. The structure of the Hamiltonian theory rules out the existence of the Newtonian limit.

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A. A. Sousa, J. W. Maluf. 2000-12-21. Canonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge. https://doi.org/10.1143/ptp.104.531

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