Derivation of Ashtekar variables from tetrad gravity

Journal Article · Sun Jan 15 04:00:00 EST 1989 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.39.434· OSTI ID:6548786

Henneaux, M; Nelson, J E; Schomblond, C

The new gravitational variables introduced recently by Ashtekar are derived from the standard tetrad gravity formalism with full local Lorentz invariance. This is done by a succession of canonical transformations, which involve as a first step the transition from arbitrary tetrads to three-dimensional triads and pure gauge boost variables. It is then shown that the weighted contravariant triads and mixed components of the extrinsic curvature are also canonically conjugate. Finally, the new variables are explicitly derived and proved to be canonical because of a remarkable identity obeyed by the spatial spin connection in three dimensions.

• Research Organization: Faculte des Sciences, Universite Libre de Bruxelles, Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium
• OSTI ID: 6548786
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 39:2; ISSN PRVDA
• Country of Publication: United States
• Language: English

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657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
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FUNCTIONS
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INVARIANCE PRINCIPLES
LORENTZ INVARIANCE
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MATHEMATICAL OPERATORS
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SPINORS
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TRANSFORMATIONS
YANG-MILLS THEORY