Triad approach to the Hamiltonian of general relativity

Details Triad approach to the Hamiltonian of general relativity Triad approach to the Hamiltonian of general relativity

Apr 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988phrvd..37.2116g&link_type=abstract

Physical Review D (Particles and Fields), Volume 37, Issue 8, 15 April 1988, pp.2116-2120

Physics

35

Canonical Formalism, Lagrangians, And Variational Principles

Scientific paper

The Sparling-Thirring forms are constructed using a connection over a frame bundle defined in terms of a spacelike triad and lapse and shift functions. From the forms, one can identify a first-order Lagrangian from which to construct the Hamiltonian using triad vector densities as basic configuration-space variables. If one uses the self-dual part of the forms, the resulting first-order Lagrangian (its imaginary part is a total divergence) leads to momenta which are the dual of the Sen connection which was introduced by Ashtekar in a spinor representation. The resulting formalism is equivalent to that of Ashtekar.

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