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

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

2000-05-19

arxiv.org/abs/gr-qc/0005085v4

Class.Quant.Grav. 17 (2000) 4255-4268

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/17/20/307

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.

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