Classical And Quantum Mechanics With Lie Algebras

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Classical And Quantum Mechanics With Lie Algebras

Author : Yair Shapira
Publisher : World Scientific
ISBN 13 : 9811240078
Total Pages : 711 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Classical And Quantum Mechanics With Lie Algebras by : Yair Shapira

Download or read book Classical And Quantum Mechanics With Lie Algebras written by Yair Shapira and published by World Scientific. This book was released on 2021-07-19 with total page 711 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to see physics in its full picture? This book offers a new approach: start from math, in its simple and elegant tools: discrete math, geometry, and algebra, avoiding heavy analysis that might obscure the true picture. This will get you ready to master a few fundamental topics in physics: from Newtonian mechanics, through relativity, towards quantum mechanics.Thanks to simple math, both classical and modern physics follow and make a complete vivid picture of physics. This is an original and unified point of view to highlighting physics from a fresh pedagogical angle.Each chapter ends with a lot of relevant exercises. The exercises are an integral part of the chapter: they teach new material and are followed by complete solutions. This is a new pedagogical style: the reader takes an active part in discovering the new material, step by step, exercise by exercise.The book could be used as a textbook in undergraduate courses such as Introduction to Newtonian mechanics and special relativity, Introduction to Hamiltonian mechanics and stability, Introduction to quantum physics and chemistry, and Introduction to Lie algebras with applications in physics.

On Realizations of Lie Algebras and Symmetries in Classical and Quantum Mechanics (II)

Author : Joe Rosen
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis On Realizations of Lie Algebras and Symmetries in Classical and Quantum Mechanics (II) by : Joe Rosen

Download or read book On Realizations of Lie Algebras and Symmetries in Classical and Quantum Mechanics (II) written by Joe Rosen and published by . This book was released on 1966 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Algebras, Cohomology, and New Applications to Quantum Mechanics,

Author : Niky Kamran
Publisher : American Mathematical Soc.
ISBN 13 : 9780821854945
Total Pages : 330 pages
Book Rating : 4.8/5 (549 download)

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Book Synopsis Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, by : Niky Kamran

Download or read book Lie Algebras, Cohomology, and New Applications to Quantum Mechanics, written by Niky Kamran and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrodinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.

Lie Algebras and Quantum Mechanics

Author : Robert Hermann
Publisher :
ISBN 13 :
Total Pages : 340 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Lie Algebras and Quantum Mechanics by : Robert Hermann

Download or read book Lie Algebras and Quantum Mechanics written by Robert Hermann and published by . This book was released on 1970 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Topics Between Classical and Quantum Mechanics

Author : Nicholas P. Landsman
Publisher : Springer Science & Business Media
ISBN 13 : 146121680X
Total Pages : 547 pages
Book Rating : 4.4/5 (612 download)

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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 and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 547 pages. 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.

Lie Groups and Quantum Mechanics

Author : D. J. Simms
Publisher : Springer
ISBN 13 : 3540358293
Total Pages : 93 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Lie Groups and Quantum Mechanics by : D. J. Simms

Download or read book Lie Groups and Quantum Mechanics written by D. J. Simms and published by Springer. This book was released on 2006-11-15 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Foundations of Quantum Theory

Author : Klaas Landsman
Publisher : Springer
ISBN 13 : 3319517775
Total Pages : 881 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Foundations of Quantum Theory by : Klaas Landsman

Download or read book Foundations of Quantum Theory written by Klaas Landsman and published by Springer. This book was released on 2017-05-11 with total page 881 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.

Geometric Phases in Classical and Quantum Mechanics

Author : Dariusz Chruscinski
Publisher : Springer Science & Business Media
ISBN 13 : 0817681760
Total Pages : 337 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Geometric Phases in Classical and Quantum Mechanics by : Dariusz Chruscinski

Download or read book Geometric Phases in Classical and Quantum Mechanics written by Dariusz Chruscinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Methods In Classical And Quantum Physics

Author : Tulsi Dass
Publisher : Universities Press
ISBN 13 : 9788173710896
Total Pages : 718 pages
Book Rating : 4.7/5 (18 download)

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Book Synopsis Mathematical Methods In Classical And Quantum Physics by : Tulsi Dass

Download or read book Mathematical Methods In Classical And Quantum Physics written by Tulsi Dass and published by Universities Press. This book was released on 1998 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to provide an adequate background for various theortical physics courses, especially those in classical mechanics, electrodynamics, quatum mechanics and statistical physics. Each topic is dealt with in a generally self-contained manner and the text is interspersed with a number of solved examples ad a large number of exercise problems.

From Classical Mechanics To Quantum Field Theory, A Tutorial

Author : Manuel Asorey
Publisher : World Scientific
ISBN 13 : 9811210500
Total Pages : 255 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis From Classical Mechanics To Quantum Field Theory, A Tutorial by : Manuel Asorey

Download or read book From Classical Mechanics To Quantum Field Theory, A Tutorial written by Manuel Asorey and published by World Scientific. This book was released on 2020-01-14 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects an extended version of the lectures delivered by the authors at the Fall Workshop on Geometry and Physics in the years 2014, 2015, 2016.It aims at introducing advanced graduate and PhD students, as well as young researchers, to current research in mathematics and physics. In particular, it fills the gap between the more physical-oriented and the more mathematical-oriented literature on quantum theory. It introduces various approaches to methods of quantization, along with their impact on modern mathematical methods.

Yangians and Classical Lie Algebras

Author : Alexander Molev
Publisher : American Mathematical Soc.
ISBN 13 : 0821843745
Total Pages : 422 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Yangians and Classical Lie Algebras by : Alexander Molev

Download or read book Yangians and Classical Lie Algebras written by Alexander Molev and published by American Mathematical Soc.. This book was released on 2007 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Yangians and twisted Yangians are remarkable associative algebras taking their origins from the work of St. Petersburg's school of mathematical physics in the 1980s. This book is an introduction to the theory of Yangians and twisted Yangians, with a particular emphasis on the relationship with the classical matrix Lie algebras.

Lie Algebras and Applications

Author : Francesco Iachello
Publisher : Springer
ISBN 13 : 3540362398
Total Pages : 196 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Lie Algebras and Applications by : Francesco Iachello

Download or read book Lie Algebras and Applications written by Francesco Iachello and published by Springer. This book was released on 2007-02-22 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, designed for advanced graduate students and post-graduate researchers, introduces Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.

Quantum Mechanics Via Lie Algebras

Author : Arnold Neumaier
Publisher :
ISBN 13 : 9783110406108
Total Pages : 500 pages
Book Rating : 4.4/5 (61 download)

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Book Synopsis Quantum Mechanics Via Lie Algebras by : Arnold Neumaier

Download or read book Quantum Mechanics Via Lie Algebras written by Arnold Neumaier and published by . This book was released on 2020-10-04 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Classical and Quantum Physics

Author : G. Marmo
Publisher : Springer Nature
ISBN 13 : 3030247481
Total Pages : 388 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Classical and Quantum Physics by : G. Marmo

Download or read book Classical and Quantum Physics written by G. Marmo and published by Springer Nature. This book was released on 2019-10-26 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos’s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.

Quantum Theory, Groups and Representations

Author : Peter Woit
Publisher : Springer
ISBN 13 : 3319646125
Total Pages : 668 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Quantum Theory, Groups and Representations by : Peter Woit

Download or read book Quantum Theory, Groups and Representations written by Peter Woit and published by Springer. This book was released on 2017-11-01 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Classical Systems in Quantum Mechanics

Author : Pavel Bóna
Publisher : Springer Nature
ISBN 13 : 3030450708
Total Pages : 243 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Classical Systems in Quantum Mechanics by : Pavel Bóna

Download or read book Classical Systems in Quantum Mechanics written by Pavel Bóna and published by Springer Nature. This book was released on 2020-06-23 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".

An Introduction to Tensors and Group Theory for Physicists

Author : Nadir Jeevanjee
Publisher : Birkhäuser
ISBN 13 : 3319147943
Total Pages : 305 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis An Introduction to Tensors and Group Theory for Physicists by : Nadir Jeevanjee

Download or read book An Introduction to Tensors and Group Theory for Physicists written by Nadir Jeevanjee and published by Birkhäuser. This book was released on 2015-03-11 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques. Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups. Reviews of the First Edition “[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.” —Physics Today "Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.” —MAA Reviews