Open AccessCanonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge
Author(s) -
A. A. Sousa,
J. W. Maluf
Publication year - 2000
Publication title -
progress of theoretical physics
Language(s) - English
Resource type - Journals
eISSN - 1347-4081
pISSN - 0033-068X
DOI - 10.1143/ptp.104.531
Subject(s) - physics , hamiltonian (control theory) , mathematical physics , covariant hamiltonian field theory , gauge theory , gravitation , spacetime , quadratic equation , poisson bracket , classical mechanics , theoretical physics , hamiltonian system , quantum mechanics , mathematics , geometry , mathematical optimization , lie algebra
We consider the most general class of teleparallel gravitational {}{}theoriesquadratic in the torsion tensor, in three space-time dimensions, and carry outa detailed investigation of its Hamiltonian formulation in Schwinger's timegauge. This general class is given by a family of three-parameter theories. Aconsistent implementation of the Legendre transform reduces the original theoryto a one-parameter family of theories. By calculating Poisson brackets we showexplicitly 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 theNewtonian limit.Comment: 17 pages, Latex file, no figures; a numerical coefficient has been corrected and a different result is achieve
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