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Mapping-Class Groups of 3-Manifolds in Canonical Quantum Gravity

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Quantum Gravity

Abstract

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.

I sincerely thank Bertfried Fauser and Jürgen Tolksdorf for organizing Blaubeuren II and inviting me to it.

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  1. Physikalisches Institut, Universität Freiburg, Hermann-Herder-Straße 3, D-79104, Freiburg, Germany

    Domenico Giulini

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  1. Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22-26, D-04103, Leipzig, Germany

    Bertfried Fauser , Jürgen Tolksdorf  & Eberhard Zeidler ,  & 

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This contribution is dedicated to Rafael Sorkin on the occasion of his 60th birthday

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Giulini, D. (2006). Mapping-Class Groups of 3-Manifolds in Canonical Quantum Gravity. In: Fauser, B., Tolksdorf, J., Zeidler, E. (eds) Quantum Gravity. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7978-0_9

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