【摘 要】
：
The space of convex polyhedra can be given a dynamical structure.Exploiting this dynamics we have performed a Bohr-Sommerfeld quantization of the volume of
【机 构】
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Centre de Physique Theorique de Luminy, France
【出 处】
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The XXIX International Colloquium on Group-Theoretical Metho
论文部分内容阅读
The space of convex polyhedra can be given a dynamical structure.Exploiting this dynamics we have performed a Bohr-Sommerfeld quantization of the volume of a tetrahedral grain of space,which is in excellent agreement with loop gravity.Here we present investigations of the volume of a 5-faced convex polyhedron.We give for the first time a constructive method for finding these polyhedra given their face areas and normals to the faces and find an explicit formula for the volume.This results in new information about cylindrical consistency in loop gravity and a couple of surprises about polyhedra.In particular,we are interested in discovering whether the evolution generated by this volume is chaotic or integrable as this will impact the interpretation of the spin network basis in loop gravity.
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