2+1 quantum gravity with a Barbero–Immirzi-like parameter on toric spatial foliation

2009/09/30 by Rudranil Basu, S. Paul, Samir K Paul · 10 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Cosmology and Gravitation Theories #Covariant transformation #Foliation (geology) #Geometry #Hilbert space #Immirzi parameter #Loop quantum gravity #Mathematical physics #Noncommutative and Quantum Gravity Theories #Parameter space #Physics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Space (punctuation) #Spin foam #Topology (electrical circuits) #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/27/12/125003

published in Classical and Quantum Gravity 27(12), 125003 (IOP Publishing) · Latex, Substantial changes: new sections added. Accepted for publication in Class. Quant. Garv.

arxiv created 2010/03/17 · openalex publication_date 2010/04/26 · arxiv updated 2010/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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<sup>2</sup> × \mathbbmR. 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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