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Geometric Formulation of Classical and Quantum Mechanics

2011 Science
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Release : 2011
Genre : Science
Kind : eBook
Book Rating : 726/5 ( reviews)

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Book Synopsis Geometric Formulation of Classical and Quantum Mechanics by : G. Giachetta

Download or read book Geometric Formulation of Classical and Quantum Mechanics written by G. Giachetta. This book was released on 2011. Available in PDF, EPUB and Kindle. Book excerpt: The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. This book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations.

Geometric Formulation Of Classical And Quantum Mechanics

2010-10-11 Science
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Release : 2010-10-11
Genre : Science
Kind : eBook
Book Rating : 554/5 ( reviews)

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Book Synopsis Geometric Formulation Of Classical And Quantum Mechanics by : Giovanni Giachetta

Download or read book Geometric Formulation Of Classical And Quantum Mechanics written by Giovanni Giachetta. This book was released on 2010-10-11. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Symplectic Geometry and Quantum Mechanics

2006-08-06 Mathematics
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Release : 2006-08-06
Genre : Mathematics
Kind : eBook
Book Rating : 752/5 ( reviews)

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Book Synopsis Symplectic Geometry and Quantum Mechanics by : Maurice A. de Gosson

Download or read book Symplectic Geometry and Quantum Mechanics written by Maurice A. de Gosson. This book was released on 2006-08-06. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.

Mathematical Topics Between Classical and Quantum Mechanics

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 80X/5 ( reviews)

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Book Synopsis Mathematical Topics Between Classical and Quantum Mechanics by : Nicholas P. Landsman

Download or read book Mathematical Topics Between Classical and Quantum Mechanics written by Nicholas P. Landsman. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability, which leads on to a discussion of the theory of quantization and the classical limit from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.

Geometrical Quantum Mechanics

2013-03-23 Science
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Release : 2013-03-23
Genre : Science
Kind : eBook
Book Rating : 045/5 ( reviews)

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Book Synopsis Geometrical Quantum Mechanics by : Robert Geroch

Download or read book Geometrical Quantum Mechanics written by Robert Geroch. This book was released on 2013-03-23. Available in PDF, EPUB and Kindle. Book excerpt: Geroch's lecture notes on geometrical quantum mechanics are divided into three parts - Differential Geometry, Mechanics, and Quantum Mechanics. The necessary geometrical ideas are presented in the first part of the book and are applied to mechanics and quantum mechanics in the second and third part. What also makes this book a valuable contribution to the existing textbooks on quantum physics is Geroch's unique approach to teaching theoretical and mathematical physics - the physical concepts and the mathematics, which describes them, are masterfully intertwined in such a way that both reinforce each other to facilitate the understanding of even the most abstract and subtle issues.

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