Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

Details Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity Gauge group and reality conditions in Ashtekar's complex formulation of canonical gravity

1999-12-20

arxiv.org/abs/gr-qc/9912085v1

Phys.Rev. D62 (2000) 064026

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Submitted to Phys. Rev. D15. - 17 pages

Scientific paper

10.1103/PhysRevD.62.064026

We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekar's complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the reality conditions, which is different from Dirac's method of stabilization of constraints. We solve the problem of the projectability of the diffeomorphism transformations from configuration-velocity space to phase space, linking them to the reality conditions. We construct the complete set of canonical generators of the gauge group in the phase space which includes all the gauge variables. This result proves that the canonical formalism has all the gauge structure of the Lagrangian theory, including the time diffeomorphisms.

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