2-categorical Poincare Representations and State Sum Applications

Details 2-categorical Poincare Representations and State Sum Applications 2-categorical Poincare Representations and State Sum Applications

2003-06-30

arxiv.org/abs/math/0306440v1

Mathematics

Quantum Algebra

16 pages, 1 figure, LaTeX

Scientific paper

This is intended as a self-contained introduction to the representation theory developed in order to create a Poincare 2-category state sum model for Quantum Gravity in 4 dimensions. We review the structure of a new representation 2-category appropriate to Lie 2-group symmetries and discuss its application to the problem of finding a state sum model for Quantum Gravity. There is a remarkable richness in its details, reflecting some desirable characteristics of physical 4-dimensionality. We begin with a review of the method of orbits in Geometric Quantization, as an aid to the intuition that the geometric picture unfolded here may be seen as a categorification of this process.

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