2-Group Representations for Spin Foams

Abstract

Just as 3d state sum models, including 3d quantum gravity, can be built using categories of group representations, "2-categories of 2-group representations" may provide interesting state sum models for 4d quantum topology, if not quantum gravity. Here we focus on the "Euclidean 2-group", built from the rotation group SO(4) and its action on the group of translations of 4d Euclidean space. We explain its infinite-dimensional unitary representations, and construct a model based on the resulting representation 2-category. This model, with clear geometric content and explicit "metric data" on triangulation edges, shows up naturally in an attempt to write the amplitudes of ordinary quantum field theory in a background independent way.

8 pages; to appear in proceedings of the XXV Max Born Symposium: "The Planck Scale", Wroclaw, Poland

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• Higher-Dimensional Algebra V: 2-Groups
• Higher Yang-Mills Theory
• Regge calculus from a new angle
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• Categorical representations of categorical groups
• A Prehistory of n-Categorical Physics
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Cited by in corpus (9)

• An Invitation to Higher Gauge Theory
• A new vacuum for Loop Quantum Gravity
• Teleparallel Gravity as a Higher Gauge Theory
• Poincare 2-group and quantum gravity
• Quantum geometry from higher gauge theory
• A 2-categorical state sum model
• Hamiltonian analysis of the BFCG theory for the Poincare 2-group
• Twisted actions of categorical groups
• Generalized Higher Gauge Theory and M5-brane dynamics. Proceedings: Higher structures in String and M-theory, Tohoku Forum for Creativity, March 7-11 2016