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Conference Paper

2-Group Representations for Spin Foams

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Baratin,  Aristide
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

0910.1542v1.pdf
(Preprint), 136KB

AIP1196_28.pdf
(Any fulltext), 2MB

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Citation

Baratin, A., & Wise, D. K. (2009). 2-Group Representations for Spin Foams. doi:10.1063/1.3284396.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-611A-F
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.