Mapping-class groups of 3-manifolds in canonical quantum gravity

Details Mapping-class groups of 3-manifolds in canonical quantum gravity Mapping-class groups of 3-manifolds in canonical quantum gravity

2006-06-29

arxiv.org/abs/math-ph/0606066v1

Physics

Mathematical Physics

41 pages, 8 figures (colored)

Scientific paper

Mapping-class groups of 3-manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries, their inequivalent unitary irreducible representations should give rise to a complex superselection structure. This highlights certain aspects of spatial diffeomorphism invariance that to some degree seem physically meaningful and which persist in all approaches based on smooth 3-manifolds, like geometrodynamics and loop quantum gravity. We also attempt to give a flavor of the mathematical ideas involved.

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