Geometric Formulation Of Classical And Quantum Mechanics
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A01=Gennadi A Sardanashvily
A01=Giovanni Giachetta
A01=Luigi Mangiarotti
Author_Gennadi A Sardanashvily
Author_Giovanni Giachetta
Author_Luigi Mangiarotti
Category=PHQ
Category=PHU
Differential Geometry
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Hamiltonian Theory
Lagrangian Theory
Mechanics
Quantum Theory
Product details
- ISBN 9789814313728
- Publication Date: 12 Oct 2010
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
