APS » PROLA » Phys. Rev. D » Volume 62 » Issue 6

Phys. Rev. D 62, 064026 (2000) [15 pages]

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

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J. M. Pons *
Departament d’Estructura i Constituents de la Matèria, Universitat de Barcelona, and Institut de Física d’Altes Energies, Diagonal 647, E-08028 Barcelona, Catalonia, Spain

D. C. Salisbury †
Department of Physics, Austin College, Sherman, Texas 75090-4440

L. C. Shepley ‡
Center for Relativity, Physics Department, The University of Texas, Austin, Texas 78712-1081

Received 2 August 1999; published 25 August 2000

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.


©2000 The American Physical Society

URL: http://link.aps.org/abstract/PRD/v62/e064026
DOI: 10.1103/PhysRevD.62.064026
PACS: 04.20.Fy, 11.10.Ef

* Electronic address: pons@ecm.ub.es
† Electronic address: dsalisbury@austinc.edu
‡ Electronic address: larry@einstein.ph.utexas.edu

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