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arXiv · 0909.4238

2+1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation

Rudranil Basu·Samir K Paul
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Abstract

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.

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Rudranil Basu, Samir K Paul. 2010-03-17. 2+1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation. https://doi.org/10.1088/0264-9381%2F27%2F12%2F125003

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