Geometric Formulation Of Classical And Quantum Mechanics PDF Download
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Author | : G. Giachetta |
Publisher | : World Scientific |
Total Pages | : 405 |
Release | : 2011 |
Genre | : Science |
ISBN | : 9814313726 |
Download Geometric Formulation of Classical and Quantum Mechanics Book in PDF, ePub and Kindle
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.
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Publisher | : |
Total Pages | : |
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ISBN | : 9814464554 |
Download Geometric Formulation of Classical and Quantum Mechanics Book in PDF, ePub and Kindle
Author | : Dariusz Chruscinski |
Publisher | : Springer Science & Business Media |
Total Pages | : 337 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817681760 |
Download Geometric Phases in Classical and Quantum Mechanics Book in PDF, ePub and Kindle
Several well-established geometric and topological methods are used in this work in an application to a beautiful physical phenomenon known as the geometric phase. This book examines the geometric phase, bringing together different physical phenomena under a unified mathematical scheme. The material is presented so that graduate students and researchers in applied mathematics and physics with an understanding of classical and quantum mechanics can handle the text.
Author | : Maurice A. de Gosson |
Publisher | : Springer Science & Business Media |
Total Pages | : 375 |
Release | : 2006-08-06 |
Genre | : Mathematics |
ISBN | : 3764375752 |
Download Symplectic Geometry and Quantum Mechanics Book in PDF, ePub and Kindle
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.
Author | : Nicholas P. Landsman |
Publisher | : Springer Science & Business Media |
Total Pages | : 547 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 146121680X |
Download Mathematical Topics Between Classical and Quantum Mechanics Book in PDF, ePub and Kindle
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.
Author | : José F. Cariñena |
Publisher | : Springer |
Total Pages | : 739 |
Release | : 2014-09-23 |
Genre | : Science |
ISBN | : 9401792208 |
Download Geometry from Dynamics, Classical and Quantum Book in PDF, ePub and Kindle
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'' and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and super integrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
Author | : Alex Harvey |
Publisher | : Springer Science & Business Media |
Total Pages | : 546 |
Release | : 1999 |
Genre | : Philosophy |
ISBN | : 9780387985640 |
Download On Einstein’s Path Book in PDF, ePub and Kindle
This collection of nearly forty essays in honor of the noted physicist and cosmologist Engelbert Schucking spans the gamut of research in Einsteins theory of general relativity and presents a lively and personal account of current work in the field. Indispensable for physicists involved in research in the field, the book includes important chapters by noted theorists such as A. Ashtekar, P.G. Bergmann, J. Ehlers, E.T. Newman, J.V. Narlikar, R. Penrose, D.W. Sciama, J. Stachel, and W. Rindler.
Author | : Robert Geroch |
Publisher | : Minkowski Institute Press |
Total Pages | : 137 |
Release | : 2013-03-23 |
Genre | : Science |
ISBN | : 1927763045 |
Download Geometrical Quantum Mechanics Book in PDF, ePub and Kindle
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.
Author | : V.S. Varadarajan |
Publisher | : Springer Science & Business Media |
Total Pages | : 426 |
Release | : 2007-12-03 |
Genre | : Science |
ISBN | : 0387493867 |
Download Geometry of Quantum Theory Book in PDF, ePub and Kindle
Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac and whose definitive mathematical formulation is due to von Neumann. This view leads most naturally to the fundamental questions that are at the basis of all attempts to understand the world of atomic and subatomic particles.
Author | : D. Chrus'cin'ski |
Publisher | : |
Total Pages | : |
Release | : 2004 |
Genre | : |
ISBN | : 9783764342821 |
Download Geometric Phases in Classical and Quantum Mechanics Book in PDF, ePub and Kindle