Reality conditions for Ashtekar variables as Dirac constraints

Abstract

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.

16 pages, plain LaTeX, submitted to Class. Quant. Grav. E-mail: [email protected]

References in corpus (6)

• Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
• Reality conditions inducing transforms for quantum gauge field theory and quantum gravity
• Reality Conditions and Ashtekar Variables: a Different Perspective
• Constraints and Reality Conditions in the Ashtekar Formulation of General Relativity
• Bibliography of Publications related to Classical and Quantum Gravity in terms of the Ashtekar Variables
• Solving the Constraints of General Relativity

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