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Geometric Formulation Of Classical And Quantum Mechanics (Hardcover)
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Geometric Formulation Of Classical And Quantum Mechanics (Hardcover)
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The geometric formulation of autonomous Hamiltonian mechanics in
the terms of symplectic and Poisson manifolds is generally
accepted. The literature on this subject is extensive. The present
book provides the geometric formulation of non-autonomous mechanics
in a general setting of time-dependent coordinate and reference
frame transformations. This formulation of mechanics as like as
that of classical field theory lies in the framework of general
theory of dynamic systems, and Lagrangian and Hamiltonian
formalisms on fiber bundles. The reader will find a strict
mathematical exposition of non-autonomous dynamic systems,
Lagrangian and Hamiltonian non-relativistic mechanics, relativistic
mechanics, quantum non-autonomous mechanics, together with a number
of advanced models - superintegrable systems, non-autonomous
constrained systems, theory of Jacobi fields, mechanical systems
with time-dependent parameters, non-adiabatic Berry phase theory,
instantwise quantization, and quantization relative to different
reference frames.
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