Geometric Quantum Mechanics
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| Author | : Jedrzej Sniatycki |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 241 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461260663 |
This book contains a revised and expanded version of the lecture notes of two seminar series given during the academic year 1976/77 at the Department of Mathematics and Statistics of the University of Calgary, and in the summer of 1978 at the Institute of Theoretical Physics of the Technical University Clausthal. The aim of the seminars was to present geometric quantization from the point of view· of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems. The group representation aspects of geometric quantiza tion as well as proofs of the existence and the uniqueness of the introduced structures can be found in the expository papers of Blattner, Kostant, Sternberg and Wolf, and also in the references quoted in these papers. The books of Souriau (1970) and Simms and Woodhouse (1976) present the theory of geometric quantization and its relationship to quantum mech anics. The purpose of the present book is to complement the preceding ones by including new developments of the theory and emphasizing the computations leading to results in quantum mechanics.
| Author | : Dariusz Chruscinski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 346 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 0817681760 |
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 | : G. Giachetta |
| Publisher | : World Scientific |
| Total Pages | : 405 |
| Release | : 2011 |
| Genre | : Science |
| ISBN | : 9814313726 |
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.
| Author | : Edoardo Ballico |
| Publisher | : Springer |
| Total Pages | : 177 |
| Release | : 2019-03-13 |
| Genre | : Science |
| ISBN | : 3030061221 |
This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from each discipline, the authors give in each contribution pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find there new open challenges for their research. At the same time, the volume can also be of use to physicists wishing to learn advanced mathematical tools, especially of differential and algebraic geometric nature.
| Author | : Maurice A. de Gosson |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 375 |
| Release | : 2006-08-06 |
| Genre | : Mathematics |
| ISBN | : 3764375752 |
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 | : Robert Geroch |
| Publisher | : Minkowski Institute Press |
| Total Pages | : 137 |
| Release | : 2013-03-23 |
| Genre | : Science |
| ISBN | : 1927763045 |
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 | : G. Giachetta |
| Publisher | : World Scientific |
| Total Pages | : 715 |
| Release | : 2005 |
| Genre | : Science |
| ISBN | : 9812701265 |
In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
| Author | : Roger Boudet |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 126 |
| Release | : 2011-06-13 |
| Genre | : Science |
| ISBN | : 3642191991 |
This book continues the fundamental work of Arnold Sommerfeld and David Hestenes formulating theoretical physics in terms of Minkowski space-time geometry. We see how the standard matrix version of the Dirac equation can be reformulated in terms of a real space-time algebra, thus revealing a geometric meaning for the “number i” in quantum mechanics. Next, it is examined in some detail how electroweak theory can be integrated into the Dirac theory and this way interpreted in terms of space-time geometry. Finally, some implications for quantum electrodynamics are considered. The presentation of real quantum electromagnetism is expressed in an addendum. The book covers both the use of the complex and the real languages and allows the reader acquainted with the first language to make a step by step translation to the second one.
| Author | : Sylvie Paycha |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 272 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : 0821840622 |
This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.
| Author | : Veeravalli S. Varadarajan |
| Publisher | : |
| Total Pages | : 255 |
| Release | : 1970 |
| Genre | : |
| ISBN | : |
