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Reality conditions for Ashtekar variables as Dirac constraints. (English) Zbl 0863.53064

Summary: We show that the reality conditions to be imposed on Ashtekar variables to recover real gravity can be implemented as second-class constraints following 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.

MSC:

53Z05 Applications of differential geometry to physics
83C45 Quantization of the gravitational field
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