Abstract
The basic physical observable quantities are usually related to groups of state space transformations, which allows us to reduce the infinite-dimensional state space of quantum mechanics to classical phase space of finite dimensional systems. Classical kinematics and dynamics of such systems is shown to be given by the underlying quantum mechanical structures. These classical mechanical systems are called here classical mechanical projections of quantum mechanical systems.
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Notes
- 1.
In the following, if not explicitly mentioned different, the word ‘neighbourhood’ in a topological space will mean ‘an open neighbourhood’.
- 2.
Remember that if \(\mathbf{x}\equiv P_x\in P(\mathcal{H})\), then \(\varvec{U}(g)\mathbf{x}\equiv P_{U(g)x}\equiv U(g)P_xU(g^{-1})\).
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Bóna, P. (2020). Classical Mechanical Projections of QM. In: Classical Systems in Quantum Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-030-45070-0_3
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DOI: https://doi.org/10.1007/978-3-030-45070-0_3
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-45069-4
Online ISBN: 978-3-030-45070-0
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