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Classical Mechanics in Hilbert Space, Part 2

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Abstract

We continue from Part 1. We will illustrate the general theory of Hamiltonian mechanics in the Lie group formalism. We then obtain the Hamiltonian formalism in the Hilbert spaces of square integrable functions on the symplectic spaces. We illustrate this general theory with several concrete examples, two of which are the representations of the Lorentz group and the Poincaré group with interactions.

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá della Calabria and Istituto Nazionale di Fisica Nucleare, via P. Bucci cubo 30-B, 87036, Arcavacata di Rende, Cosenza, Italy

    Roberto Beneduci

  2. Applied Mathematics and Mathematical Physics Department of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada

    James Brooke

  3. Department of Mathematics, University of Denver, 2360 S. Gaylord Street, Denver, CO, USA

    Ray Curran & Franklin E. Schroeck Jr.

Authors
  1. Roberto Beneduci
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  2. James Brooke
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  3. Ray Curran
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  4. Franklin E. Schroeck Jr.
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Correspondence to Roberto Beneduci.

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Beneduci, R., Brooke, J., Curran, R. et al. Classical Mechanics in Hilbert Space, Part 2. Int J Theor Phys 50, 3697–3723 (2011). https://doi.org/10.1007/s10773-011-0869-9

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  • DOI: https://doi.org/10.1007/s10773-011-0869-9

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