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Generating functions for the affine symplectic group

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Abstract

The generating function notion is used to give a representation of the inhomogeneous symplectic group as group of affine canonical transformations. Then the classical action for linear mechanical systems, the Hamiltonians of which belong to the algebrah sp(2n,R), is deduced; it is explicitely constructed for all the Hamiltonians belonging to some particular subalgebras ofh sp(2n,R). The metaplectic representation ofW Sp(2n,R) onL 2(R) and the solutions of the Schrödinger equation for linear systems are also obtained in terms of generating functions. The Maslov index is explicitly constructed for the quantum corresponding sets of Hamiltonians considered in the classical case.

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Author notes

  1. G. Burdet & M. Perrin

    Present address: Laboratoire de Physique Mathématiques, Faculté des Sciences Mirande, F-21000, Dijon, France

Authors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, H3C3J7, Montréal, Canada

    G. Burdet, M. Perrin & M. Perroud

  2. Département de Mathématiques, Université de Montréal, H3C 3J7, Montréal, Canada

    G. Burdet

Authors
  1. G. Burdet
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  2. M. Perrin
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  3. M. Perroud
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Additional information

Communicated by W. Hunziker

Members of the Centre National de la Recherche Scientifique (France)

Recipient of aid from the Ministère de l'Education du Gouvernement du Québec

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Burdet, G., Perrin, M. & Perroud, M. Generating functions for the affine symplectic group. Commun.Math. Phys. 58, 241–254 (1978). https://doi.org/10.1007/BF01614222

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  • DOI: https://doi.org/10.1007/BF01614222

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