Reality conditions for Ashtekar variables as Dirac constraints

Details Reality conditions for Ashtekar variables as Dirac constraints Reality conditions for Ashtekar variables as Dirac constraints

1996-07-21

arxiv.org/abs/gr-qc/9607044v1

Class.Quant.Grav. 13 (1996) 2933-2940

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, plain LaTeX, submitted to Class. Quant. Grav. E-mail: hugo@xanum.uam.mx

Scientific paper

10.1088/0264-9381/13/11/009

We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second class constraints a la Dirac. Thus, counting gravitational degrees of freedom follows accordingly. Some constraints of the real theory turn out to be non-polynomial, regardless of the form, polynomial or non-polynomial, taken for the reality conditions. We comment upon the compatibility of our approach with the recently proposed Wick transform point of view, as well as on some alternatives for dealing with such second class constraints.

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