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arXiv · 1409.7117

Symplectic and Semiclassical Aspects of the Schl\"afli Identity

Hal M. Haggard·Austin Hedeman·Eugene Kur·Robert G. Littlejohn
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Abstract

The Schl\"afli 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, 3-dimensional space. In this case a proof is given, based on symplectic geometry. A series of symplectic and Lagrangian manifolds related to the Schl\"afli identity, including several versions of a Lagrangian manifold of tetrahedra, are discussed. Semiclassical interpretations of the various steps are provided. Possible generalizations to 3-dimensional spaces of constant (nonzero) curvature, involving Poisson-Lie groups and q-deformed spin networks, are discussed.

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Hal M. Haggard, Austin Hedeman, Eugene Kur, Robert G. Littlejohn. 2014-09-24. Symplectic and Semiclassical Aspects of the Schl\"afli Identity. https://doi.org/10.1088/1751-8113/48/10/105203

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