2-Group Representations for Spin Foams

Details 2-Group Representations for Spin Foams 2-Group Representations for Spin Foams

2009-10-08

arxiv.org/abs/0910.1542v1

AIP Conf. Proc.1196:28-35, 2009

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1063/1.3284396

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.

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