Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-09-23
Class.Quant.Grav.27:125003,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latex, Substantial changes: new sections added. Accepted for publication in Class. Quant. Garv.
Scientific paper
10.1088/0264-9381/27/12/125003
We consider gravity in 2+1 space-time dimensions, with negative cosmological constant and a `Barbero-Immirzi' (B-I) like parameter, when the space-time topology is of the form $ T^2 \times \mathbbm{R}$. The phase space structure, both in covariant and canonical framework is analyzed. Full quantization of the theory in the 'constrain first' approach reveals a finite dimensional physical Hilbert space. An explicit construction of wave functions is presented. The dimension of the Hilbert space is found to depend on the `Barbero-Immirzi' like parameter in an interesting fashion. Comparative study of this parameter in light of some of the recent findings in literarure for similar theories is presented.
Basu Rudranil
Paul Samir K.
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