General relativity without the metric

Details General relativity without the metric General relativity without the metric

Nov 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrvl..63.2325c&link_type=abstract

Physical Review Letters, Volume 63, Issue 21, November 20, 1989, pp.2325-2328

Physics

115

Fundamental Problems And General Formalism, Canonical Formalism, Lagrangians, And Variational Principles

Scientific paper

A new class of generally covariant gauge theories is introduced. The only field in addition to the gauge connection is a scalar-density Lagrange multiplier. For the group SO(3,C) [SO(3,R)] in four dimensions and particular coupling constants, the theory is equivalent to complex [Euclidean] general relativity, modulo an important degeneracy. The spacetime metric is constructed from the curvature in a solution. A canonical analysis leads directly to Ashtekar's Hamiltonian formalism. The general solution to the four diffeomorphism constraints in the nondegenerate case is given.

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