PIRSA:12050084

Pentahedral Volume, Chaos, and Quantum Gravity

Haggard, H. (2012). Pentahedral Volume, Chaos, and Quantum Gravity. Perimeter Institute. https://pirsa.org/12050084

Haggard, Hal. Pentahedral Volume, Chaos, and Quantum Gravity. Perimeter Institute, May. 30, 2012, https://pirsa.org/12050084 

          @misc{ pirsa_PIRSA:12050084,
            doi = {10.48660/12050084},
            url = {https://pirsa.org/12050084},
            author = {Haggard, Hal},
            keywords = {Quantum Gravity},
            language = {en},
            title = {Pentahedral Volume, Chaos, and Quantum Gravity},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {may},
            note = {PIRSA:12050084 see, \url{https://pirsa.org}}
          }

Hal Haggard

Bard College

Talk number
PIRSA:12050084
Collection
Talk Type
Subject
Abstract
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.