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

Abstract

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.

Submitted to Phys. Rev. D15. - 17 pages

References in corpus (4)

• Gauge Transformations in Einstein-Yang-Mills Theories
• The gauge group in the real triad formulation of general relativity
• Gauge symmetries in Ashtekar's formulation of general relativity
• Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism

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