Symplectic and Semiclassical Aspects of the Schl\"afli Identity

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.Comment: 40 pages, 8 figure

Collaborative searching for video using the Físchlár system and a DiamondTouch table

Fischlar DT is one of a family of systems which support interactive searching and browsing through an archive of digital video information. Previous Fischlar systems have used a conventional screen, keyboard and mouse interface, but Fischlar-DT operates with using a horizontal, multiuser, touch sensitive tabletop known as a DiamondTouch. We present the Fischlar-DT system partly from a systems perspective, but mostly in terms of how its design and functionality supports collaborative searching. The contribution of the paper is thus the introduction of Fischlar-DT and a description of how design concerns for supporting collaborative search can be realised on a tabletop interface