SO(4,C)-covariant Ashtekar-Barbero gravity and the Immirzi parameter

Abstract

An so(4,C)-covariant hamiltonian formulation of a family of generalized Hilbert-Palatini actions depending on a parameter (the so called Immirzi parameter) is developed. It encompasses the Ashtekar-Barbero gravity which serves as a basis of quantum loop gravity. Dirac quantization of this system is constructed. Next we study dependence of the quantum system on the Immirzi parameter. The path integral quantization shows no dependence on it. A way to modify the loop approach in the accordance with the formalism developed here is briefly outlined.

14 pages, LATEX; minor changes; misprints corrected; commutator of two secondary second class constraints corrected

References in corpus (3)

• Quantum Geometry and Black Hole Entropy
• The Immirzi parameter in quantum general relativity
• Path integral for the Hilbert-Palatini and Ashtekar gravity

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