Geometric formulation of classical and quantum mechanics

The geometric formulation of autonomous Hamiltonian mechanics in the terms ofsymplectic and Poisson manifolds is generally accepted. The literature on this subject is extensive. The present book provides the geometric formulation ofnon-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. INDICE: Dynamic Equations; Lagrangian Mechanics; Hamiltonian Mechanics; Algebraic Quantization; Geometric Quantization; Constrained Hamiltonian Systems;Integrable Hamiltonian Systems; Jacobi Fields; Mechnics with Time-Dependent Parameters; Relativistic Mechanics; Apendices.

• ISBN: 978-981-4313-72-8
• Editorial: World Scientific
• Encuadernacion: Cartoné
• Páginas: 404
• Fecha Publicación: 01/12/2010
• Nº Volúmenes: 1
• Idioma: Inglés