Phys. Rev. Lett. 63, 2325–2328 (1989)General relativity without the metricReceived 20 September 1989; published in the issue dated 20 November 1989 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. © 1989 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.63.2325
DOI:
10.1103/PhysRevLett.63.2325
PACS:
04.20.Cv, 04.20.Fy
See AlsoComment: Eckehard W. Mielke and Friedrich W. Hehl, Comment on ‘‘General relativity without the metric’’, Phys. Rev. Lett. 67, 1370 (1991). |
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