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Classical Mechanics in Hilbert Space, Part 2

2011; Springer Science+Business Media; Volume: 50; Issue: 12 Linguagem: Inglês

10.1007/s10773-011-0869-9

0020-7748

Roberto Beneduci, J. A. Brooke, Ray Curran, Franklin E. Schroeck,

Advanced Topics in Algebra

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.