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Grasping rules and semiclassical limit of the geometry in the Ponzano–Regge model

Jonathan Hackett and Simone Speziale

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We show how the expectation values of geometrical quantities in 3D quantum gravity can be explicitly computed using grasping rules. We compute the volume of a labelled tetrahedron using the triple grasping. We show that the large spin expansion of this value is dominated by the classical expression, and we study the next to leading order quantum corrections.


PACS

04.60.Pp Loop quantum gravity, quantum geometry, spin foams

03.65.Sq Semiclassical theories and applications

MSC

83C27 Lattice gravity, Regge calculus and other discrete methods

81S10 Geometry and quantization, symplectic methods (See also 53D50)

81Q20 Semiclassical techniques including WKB and Maslov methods

Subjects

Gravitation and cosmology

Quantum information and quantum mechanics

Dates

Issue 6 (21 March 2007)

Received 27 November 2006, in final form 30 January 2007

Published 6 March 2007



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