Titlebook: Geometric Phases in Classical and Quantum Mechanics; Dariusz Chru?ciński,Andrzej Jamio?kowski Textbook 2004 Springer Science+Business Medi

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Textbook 2004adiabatic phase and its generalization are introduced. ...? Systematic exposition treats different geometries (e.g., symplectic and metric structures) living on a quantum phase space, in connection with both abelian and nonabelian phases. ...? Quantum mechanics is presented as classical Hamiltonian

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1544-9998 ifferent geometries (e.g., symplectic and metric structures) living on a quantum phase space, in connection with both abelian and nonabelian phases. ...? Quantum mechanics is presented as classical Hamiltonian 978-1-4612-6475-0978-0-8176-8176-0Series ISSN 1544-9998 Series E-ISSN 2197-1846

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https://doi.org/10.1007/978-3-540-75736-8unt dynamical effects but in the limit of infinitely slow changes. That is, the system is no longer static but its evolution is “infinitely slow.” A typical situation where one applies adiabatic ideas is when a physical system may be divided into two subsystems with completely different time scales:

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https://doi.org/10.1007/978-3-662-64457-7What could be a classical analog of the quantum geometric phase? An obvious candidate, which is even called a phase, is the phase of harmonic motion:

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https://doi.org/10.1007/978-3-642-18600-4Suppose that (., Ω) is a symplectic manifold and let . be a Lie group acting from the left on .by canonical transformations. That is, there is a mapping . such that for any . ∈ ., . defined by Φ. = Φ(., ·), is a canonical transformation:

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