2-Group Representations for Spin Foams

Journal Article · Tue Dec 15 00:00:00 EST 2009 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3284396· OSTI ID:21371379

Baratin, Aristide ^[1]; Wise, Derek K ^[2]

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1. Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muehlenberg 1, 14467 Golm (Germany)
2. Department of Mathematics, University of California, Davis, 95616 (United States)

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 translation group R{sup 4} of 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.

• OSTI ID: 21371379
• Journal Information: AIP Conference Proceedings, Vol. 1196, Issue 1; Conference: 25. Max Born symposium, Wroclaw (Poland), 29 Jun - 3 Jul 2009; Other Information: DOI: 10.1063/1.3284396; (c) 2009 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
EUCLIDEAN SPACE
GEOMETRY
HILBERT SPACE
METRICS
QUANTUM GRAVITY
ROTATION
SO-4 GROUPS
SPIN
TOPOLOGY
ANGULAR MOMENTUM
BANACH SPACE
FIELD THEORIES
LIE GROUPS
MATHEMATICAL SPACE
MATHEMATICS
MOTION
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
RIEMANN SPACE
SO GROUPS
SPACE
SYMMETRY GROUPS