2-categorical Poincare Representations and State Sum Applications

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.

16 pages, 1 figure, LaTeX

References in corpus (7)

• Two Dimensional Gauge Theories Revisited
• Spin Foam Models for Quantum Gravity
• Higher Yang-Mills Theory
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• A More Sensitive Lorentzian State Sum
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• Categorical representations of categorical groups
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• Infinite-Dimensional Representations of 2-Groups
• Poincare 2-group and quantum gravity
• From Loop Space Mechanics to Nonabelian Strings
• Spin-cube Models of Quantum Gravity
• A 2-categorical state sum model
• Fluxes, bundle gerbes and 2-Hilbert spaces
• 2-Group Representations for Spin Foams
• Knot theory and a physical state of quantum gravity
• Non-Hausdorff Symmetries of C*-algebras
• Extended TQFT's and Quantum Gravity
• Twisted actions of categorical groups
• On Double Groups and the Poincaré group
• Quantum gravity and elementary particles from higher gauge theory
• Generalized Higher Gauge Theory and M5-brane dynamics. Proceedings: Higher structures in String and M-theory, Tohoku Forum for Creativity, March 7-11 2016
• Construction and examples of higher gauge theories