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2-categorical Poincare Representations and State Sum Applications

L. Crane·M. D. Sheppeard
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Abstract

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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L. Crane, M. D. Sheppeard. 2003-06-30. 2-categorical Poincare Representations and State Sum Applications. https://arxiv.org/abs/math/0306440

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