Algebraic Methods In Physics
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Algebraic Methods In Physics
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Author : Yvan Saint-Aubin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Algebraic Methods In Physics written by Yvan Saint-Aubin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical physics, particularly to the study of algebraic methods.
Algebraic Methods In Quantum Chemistry And Physics
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Author : Francisco M. Fernandez
language : en
Publisher: CRC Press
Release Date : 2020-01-16
Algebraic Methods In Quantum Chemistry And Physics written by Francisco M. Fernandez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Mathematics categories.
Algebraic Methods in Quantum Chemistry and Physics provides straightforward presentations of selected topics in theoretical chemistry and physics, including Lie algebras and their applications, harmonic oscillators, bilinear oscillators, perturbation theory, numerical solutions of the Schrödinger equation, and parameterizations of the time-evolution operator. The mathematical tools described in this book are presented in a manner that clearly illustrates their application to problems arising in theoretical chemistry and physics. The application techniques are carefully explained with step-by-step instructions that are easy to follow, and the results are organized to facilitate both manual and numerical calculations. Algebraic Methods in Quantum Chemistry and Physics demonstrates how to obtain useful analytical results with elementary algebra and calculus and an understanding of basic quantum chemistry and physics.
Algebraic Methods In Statistical Mechanics And Quantum Field Theory
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Author : Dr. Gérard G. Emch
language : en
Publisher: Courier Corporation
Release Date : 2014-08-04
Algebraic Methods In Statistical Mechanics And Quantum Field Theory written by Dr. Gérard G. Emch and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-04 with Science categories.
This systematic algebraic approach offers a careful formulation of the problems' physical motivations as well as self-contained descriptions of the mathematical methods for arriving at solutions. 1972 edition.
Algebraic And Geometric Methods In Mathematical Physics
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Author : Anne Boutet de Monvel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Algebraic And Geometric Methods In Mathematical Physics written by Anne Boutet de Monvel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
Topological And Algebraic Methods In Contemporary Mathematical Physics
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Author : B. A. Dubrovin
language : en
Publisher:
Release Date : 2003
Topological And Algebraic Methods In Contemporary Mathematical Physics written by B. A. Dubrovin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Geometry, Algebraic categories.
This volume is a classic survey of algebraic geometry and topological methods in various problems of mathematical physics and provides an excellent reference text for graduate students and researchers. The book is divided into three sections: the first part concerns Hamiltonian formalism and methods that generalise Morse for certain dynamical systems of physical origin; the second part presents algebraic geometry analysis of the Yang-Baxter equations for two dimensional models; part three presents the theory of multidimensional theta functions of Abel, Riemann, Poincare in a form that is elementary and convenient for applications.
Modern Group Theoretical Methods In Physics
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Author : J. Bertrand
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Modern Group Theoretical Methods In Physics written by J. Bertrand and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
This book contains the proceedings of a meeting that brought together friends and colleagues of Guy Rideau at the Université Denis Diderot (Paris, France) in January 1995. It contains original results as well as review papers covering important domains of mathematical physics, such as modern statistical mechanics, field theory, and quantum groups. The emphasis is on geometrical approaches. Several papers are devoted to the study of symmetry groups, including applications to nonlinear differential equations, and deformation of structures, in particular deformation-quantization and quantum groups. The richness of the field of mathematical physics is demonstrated with topics ranging from pure mathematics to up-to-date applications such as imaging and neuronal models. Audience: Researchers in mathematical physics.
Physics With Maple
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Author : Frank Y. Wang
language : en
Publisher: John Wiley & Sons
Release Date : 2008-09-26
Physics With Maple written by Frank Y. Wang and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-26 with Science categories.
Written by an experienced physicist who is active in applying computer algebra to relativistic astrophysics and education, this is the resource for mathematical methods in physics using MapleTM and MathematicaTM. Through in-depth problems from core courses in the physics curriculum, the author guides students to apply analytical and numerical techniques in mathematical physics, and present the results in interactive graphics. Around 180 simulating exercises are included to facilitate learning by examples. This book is a must-have for students of physics, electrical and mechanical engineering, materials scientists, lecturers in physics, and university libraries. * Free online MapleTM material at http://www.wiley-vch.de/templates/pdf/maplephysics.zip * Free online MathematicaTM material at http://www.wiley-vch.de/templates/pdf/physicswithmathematica.zip * Solutions manual for lecturers available at www.wiley-vch.de/supplements/
Lie Algebraic Methods In Integrable Systems
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Author : Amit K. Roy-Chowdhury
language : en
Publisher: CRC Press
Release Date : 1999-09-28
Lie Algebraic Methods In Integrable Systems written by Amit K. Roy-Chowdhury and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-28 with Mathematics categories.
Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems. The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool. The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the "soldering" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.
New Mathematical Methods For Physics
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Author : Jean-Francois Pommaret
language : en
Publisher:
Release Date : 2018-06
New Mathematical Methods For Physics written by Jean-Francois Pommaret and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06 with Mathematical physics categories.
The concept of "group" has been introduced in mathematics for the first time by E. Galois (1830) and slowly passed from algebra to geometry with the work of S. Lie on Lie groups (1880) and Lie pseudogroups (1890) of transformations. The concept of a finite length differential sequence, now called the Janet sequence, had been described for the first time by M. Janet (1920). Then, the work of D. C. Spencer (1970) has been the first attempt to use the formal theory of systems of partial differential equations (PDE) in order to study the formal theory of Lie pseudogroups. However, the linear and nonlinear Spencer sequences for Lie pseudogroups, though never used in physics, largely supersede the "Cartan structure equations " (1905) and are quite different from the "Vessiot structure equations " (1903), introduced for the same purpose but never acknowledged by E. Cartan or successors. Meanwhile, mixing differential geometry with homological algebra, M. Kashiwara (1970) created "algebraic analysis" in order to study differential modules and double duality. By chance, unexpected arguments have been introduced by the brothers E. and F. Cosserat (1909) in order to revisit elasticity and by H. Weyl (1918) in order to revisit electromagnetism through a unique differential sequence only depending on the structure of the conformal group of space-time.The classical Galois theory deals with certain finite algebraic extensions and establishes a bijective order reversing correspondence between the intermediate fields and the subgroups of a group of permutations called the Galois group of the extension. It has been the dream of many mathematicians at the end of the nineteenth century to generalize these results to systems of linear or algebraic PDE and the corresponding finitely generated differential extensions, in order to be able to add the word differential in front of any classical statement. The achievement of the Picard-Vessiot theory by E. Kolchin and coworkers between 1950 and 1970 is now well-known. However, the work of Vessiot on the differential Galois theory (1904), that is on the possibility to extend the classical Galois theory to systems of algebraic PDE and algebraic Lie pseudogroups, namely groups of transformations solutions for systems of algebraic PDE, has also never been acknowledged. His main idea has been to notice that the Galois theory (old and new) is a study of principal homogeneous spaces (PHS) for algebraic groups or pseudogroups described by what he called "automorphic systems" of PDE.The purpose of this book is first to revisit Gauge Theory and General Relativity in light of the latest developments just described and then to apply the differential Galois theory in order to revisit various domains of mechanics (Shell theory, Chain theory, Frenet-Serret formulas, Hamilton-Jacobi equations). All the results presented are new. (Nova)
Mathematical Methods
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Author : Sadri Hassani
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-08
Mathematical Methods written by Sadri Hassani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-08 with Science categories.
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.