The reality conditions for the new canonical variables of general relativity
- 1 November 1993
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 10 (11) , 2347-2352
- https://doi.org/10.1088/0264-9381/10/11/017
Abstract
We examine the constraints and the reality conditions that have to be imposed in the canonical theory of four-dimensional gravity formulated in terms of Ashtekar variables. We find that the polynomial reality conditions are consistent with the constraints and make the theory equivalent to Einstein's, as long as the densitized inverse 3-metric is positive definite; in a region of space where it is not, the theory is still consistent, although it does not describe (in general) a real local geometry.Keywords
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This publication has 14 references indexed in Scilit:
- Degenerate metrics and an empty black holeClassical and Quantum Gravity, 1991
- Ashtekar formulation of general relativity and loop-space nonperturbative quantum gravity: a reportClassical and Quantum Gravity, 1991
- Topology change in classical and quantum gravityClassical and Quantum Gravity, 1991
- New variables for gravity: Inclusion of matterPhysical Review D, 1989
- 2 + 1 dimensional gravity as an exactly soluble systemNuclear Physics B, 1988
- Covariant action for Ashtekar's form of canonical gravityClassical and Quantum Gravity, 1988
- New Hamiltonian formulation of general relativityPhysical Review D, 1987
- A lagrangian basis for ashtekar’s reformulation of canonical gravityPramana, 1987
- New Variables for Classical and Quantum GravityPhysical Review Letters, 1986
- Gravity theories with asymptotically flat instantonsNuclear Physics B, 1982