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Hamiltonian Structure of 2+1 Dimensional Gravity

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Recent Developments in General Relativity, Genoa 2000

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Abstract

A summary is given of some results and perspectives of the hamiltonian ADM approach to 2 + 1 dimensional gravity. After recalling the classical results for closed universes in the absence of matter, we go over the the case in which matter is present in the form of point spinless particles. Here the maximally slicing gauge proves most effective by relating 2 + 1 dimensional gravity to the Riemann-Hilbert problem. It is possible to solve the gravitational field in terms of the particle degrees of freedom thus reaching a reduced dynamics which involves only the particle positions and momenta. Such a dynamics is proven to be hamiltonian and the hamiltonian is given by the boundary term in the gravitational action. As an illustration, the two body hamiltonian is used to provide the canonical quantization of the two particle system.

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Authors and Affiliations

  1. Dipartimento di Fisica dell’Universitá, and INFN Sezione di Pisa, Via F. Buonarroti 2, 56100, Pisa, Italy

    P. Menotti

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  1. P. Menotti
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Correspondence to P. Menotti .

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Editors and Affiliations

  1. Dipartimento di Metodi e Modelli Matematici (DIMET), Università di Genova, Genova, Italy

    R. Cianci

  2. Dipartimento di Fisica, Università di Genova and Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Genova, Italy

    R. Collina

  3. Dipartimento di Matematica, Università di Torino, Torino, Italy

    M. Francaviglia

  4. Dipartimento di Fisica Teorica, Università di Torino and Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Torino, Italy

    P. Fré

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Menotti, P. (2002). Hamiltonian Structure of 2+1 Dimensional Gravity. In: Cianci, R., Collina, R., Francaviglia, M., Fré, P. (eds) Recent Developments in General Relativity, Genoa 2000. Springer, Milano. https://doi.org/10.1007/978-88-470-2101-3_12

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  • DOI: https://doi.org/10.1007/978-88-470-2101-3_12

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-0162-6

  • Online ISBN: 978-88-470-2101-3

  • eBook Packages: Springer Book Archive

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