Classical mechanics in Hilbert space. II. (English) Zbl 1266.70029
Summary: We continue from Part 1 [ibid. 50, No. 12, 3682–3696 (2011; Zbl 1266.70030)]. 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.
MSC:
| 70H05 | Hamilton’s equations |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 47N99 | Miscellaneous applications of operator theory |
| 70G65 | Symmetries, Lie group and Lie algebra methods for problems in mechanics |
| 81S05 | Commutation relations and statistics as related to quantum mechanics (general) |
Citations:
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