Symplectic and semiclassical aspects of the Schläfli identity. (19th February 2015)

• Record Type: Journal Article
• Authors: Hedeman, Austin; Kur, Eugene; Littlejohn, Robert G; Haggard, Hal M
• Is Part Of: Journal of physics. Volume 48:Number 10(2015)
• Publication Date: 2015-02-19
• Subjects: Schläfli identity -- 6j symbol -- semiclassical mechanics -- Regge calculus -- quantum gravity; 04.60.Nc -- 04.60.Pp -- 02.40.Yy -- 03.65.Sq; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/10/105203
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: The Schläfli identity, which is important in Regge calculus and loop quantum gravity, is examined from a symplectic and semiclassical standpoint in the special case of flat, three-dimensional space. In this case a proof is given, based on symplectic geometry. A series of symplectic and Lagrangian manifolds related to the Schläfli identity, including several versions of a Lagrangian manifold of tetrahedra, are discussed. Semiclassical interpretations of the various steps are provided. Possible generalizations to three-dimensional spaces of constant (nonzero) curvature, involving Poisson–Lie groups and q -deformed spin networks, are discussed.