This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws.
Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
Numerous enhancements and revision are incorporated into this new edition. For example, fiber bundle techniques are used to introduce differential geometry. This more elegant and intuitive approach naturally connects differential geometry with not only the general theory of relativity, but also gauge theories of fundamental forces.
Some praise for the previous edition:
PAGEOPH Pure and Applied Geophysics]
Review by Daniel Wojcik, University of Maryland
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
..". Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics studen
Автор: Alexander S. Holevo Название: Quantum Systems, Channels, Information: A Mathematical Introduction ISBN: 311027325X ISBN-13(EAN): 9783110273250 Издательство: Walter de Gruyter Цена: 16916.00 р. 24166.00-30% Наличие на складе: Есть (1 шт.) Описание: The main emphasis of this work is the mathematical theory of quantum channels and their entropic and information characteristics. Quantum information theory is one of the key research areas, since it leads the way to vastly increased computing speeds by using quantum systems to store and process information. Quantum cryptography allows for secure communication of classified information. Research in the field of quantum informatics, including quantum information theory, is in progress in leading scientific centers throughout the world.The past years were marked with impressive progress made by several researchers in solution of some difficult problems, in particular, the additivity of the entropy characteristics of quantum channels. This suggests a need for a book that not only introduces the basic concepts of quantum information theory, but also presents in detail some of the latest achievements.
Описание: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob . Titles in planning include Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures, and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic and Computational Models for Fractional Calculus , second edition (2020) Mariusz Lemanczyk, Ergodic Theory: Spectral Theory, Joinings, and Their Applications (2020) Marco Abate, Holomorphic Dynamics on Hyperbolic Complex Manifolds (2021) Miroslava Antic, Joeri Van der Veken, and Luc Vrancken, Differential Geometry of Submanifolds: Submanifolds of Almost Complex Spaces and Almost Product Spaces (2021) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.
The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.
Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.
Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.
Описание: This book collects lectures given by the plenary speakers at the 10th International ISAAC Congress, held in Macau, China in 2015. The contributions, authored by eminent specialists, present some of the most exciting recent developments in mathematical analysis, probability theory, and related applications. Topics include: partial differential equations in mathematical physics, Fourier analysis, probability and Brownian motion, numerical analysis, and reproducing kernels. The volume also presents a lecture on the visual exploration of complex functions using the domain coloring technique. Thanks to the accessible style used, readers only need a basic command of calculus.
This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.
Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.
This volume presents a collection of problems and solutions in differential geometry with applications. Both introductory and advanced topics are introduced in an easy-to-digest manner, with the materials of the volume being self-contained. In particular, curves, surfaces, Riemannian and pseudo-Riemannian manifolds, Hodge duality operator, vector fields and Lie series, differential forms, matrix-valued differential forms, Maurer-Cartan form, and the Lie derivative are covered.
Readers will find useful applications to special and general relativity, Yang-Mills theory, hydrodynamics and field theory. Besides the solved problems, each chapter contains stimulating supplementary problems and software implementations are also included. The volume will not only benefit students in mathematics, applied mathematics and theoretical physics, but also researchers in the field of differential geometry.
Автор: Vladimir Dobrev Название: Lie Theory and Its Applications in Physics ISBN: 9811096732 ISBN-13(EAN): 9789811096730 Издательство: Springer Рейтинг: Цена: 27950.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Luigi Accardi, Abdessatar Barhoumi, Yun Gang Lu, andMohamed Rhaima: *-Lie Algebras Canonically Associated to Probability Measures on R with All Moments.- Loriano Bonora: Special Conformal Transformations and Contact Terms.- Ivan Dimitrijevic, Branko Dragovich, Jelena Stankovic, Alexey S. Koshelev, and Zoran Rakic: On Nonlocal Modified Gravity and Its Cosmological Solutions.- Malte Henkel: Kinetics of Interface Growth: Physical Ageing and Dynamical Symmetries.- Evgeny Ivanov and Stepan Sidorov: News on SU(21) Supersymmetric Mechanics.- Toshiyuki Kobayashi: Intrinsic Sound of Anti-de Sitter Manifolds.- Efrat Gerchkovitz and Zohar Komargodski: Sphere Partition Functions and the Kahler Metric on the Conformal Manifold.- Mikhail V. Ignatyev, Ivan Penkov, and Joseph A. Wolf: Real Group Orbits on Flag Ind-Varieties of SL(∞, C).- Raul Gomez and Birgit Speh: Derived functors and Intertwining operators for Principal Series Representations of SL2(R).- Ivan Todorov: Hyperlogarithms and Periods in Feynman Amplitudes.- N.I. Stoilova and J. Van der Jeugt: The Parastatistics Fock Space and Explicit Infinite-Dimensional Representations of the Lie Superalgebra osp(2m+12n).- Joseph A. Wolf: Stepwise Square Integrable Representations: the Concept and Some Consequences.- G. Manolakos and G. Zoupanos: Higher-Dimensional Unified Theories with Continuous and Fuzzy Coset Spaces as Extra Dimensions.- Fumihiko Sugino: Higher Genus Amplitudes in SUSY Double-Well Matrix Model for 2D IIA Superstring.- Eduardo Guendelman, Emil Nissimov, Svetlana Pacheva, and Michail Stoilov: Kruskal-Penrose Formalism for Lightlike Thin-Shell Wormholes.- Eduardo Guendelman, Emil Nissimov, and Svetlana Pacheva: Metric-Independent Spacetime Volume-Forms and Dark Energy/Dark Matter Unification.- Hervй Partouche: Large Volume Supersymmetry Breaking without Decompactification Problem.- Lilia Anguelova: Glueball Inflation and Gauge/Gravity Duality.- Ovidiu Cristinel Stoica: Degenerate Metrics and Their Applications to Spacetime.- Denitsa Staicova and Plamen Fiziev: The Heun Functions and Their Applications in Astrophysics.- Chihiro Matsui: Boundary Effects on the Supersymmetric Sine-Gordon Model through Light-cone Lattice Regularization.- Roberto Bondesan and Thomas Quella: Infinite Dimensional Matrix Product States for Long-Range Quantum Spin Models.- Olena Vaneeva, Yuri Karadzhov, and Christodoulos Sophocleous: Group Analysis of a Class of Nonlinear Kolmogorov Equations.- Lachezar S. Georgiev: Thermoelectric Characteristics of Zk Parafermion Coulomb Islands.- Paolo Lorenzoni and Andrea Savoldi: First Order Hamiltonian Operators of Differential-Geometric Type in 2D.- Oksana Kuriksha and Olena Magda: Exact Solutions for Generalized KdV Equations with Variable Coefficients Using the Equivalence Method.- Pavle Pandzic: Classifying Aq(λ) Modules by Their Dirac Cohomology.- Nurit Barnea and Anna Melnikov: B-orbits in Abelian Nilradicals of Types B, C and D: Towards a Conjecture of Panyushev.- Vladimir K. Dobrev and Patrick Moylan: Anti de Sitter Holography via Sekiguchi Decomposition.- Patrick Moylan: Localization and the Canonical Commutation Relations.- Igor Salom and V. Dmitrasinovic: Permutation-Symmetric Three-Body O(6) Hyperspherical Harmonics in Three Spatial Dimensions.- Todor Popov: Quantum Plactic and Pseudo-Plactic Algebras.- Stoimen Stoimenov and Malte Henkel: Conformal Invariance of the 1D Collisionless Boltzmann Equation.- Toshihisa Kubo: On Reducibility Criterions for Scalar Generalized Verma Modules Associated to Maximal Parabolic Subalgebras.-&n
Автор: Schwalm A Название: Lectures on Selected Topics in Mathematical Physics ISBN: 1681741660 ISBN-13(EAN): 9781681741666 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 5405.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offers a basic introduction to certain aspects of elliptic functions and elliptic integrals. The lectures contained in this text introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This method depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject.
Автор: Michael Ruzhansky, Hemen Dutta, Ravi P. Agarwal Название: Mathematical Analysis and Applications: Selected Topics ISBN: 1119414342 ISBN-13(EAN): 9781119414346 Издательство: Wiley Рейтинг: Цена: 18525.00 р. Наличие на складе: Поставка под заказ.
Описание: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research
Mathematical Analysis and ApplicationsSelected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss-Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors--a noted team of international researchers in the field-- highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text:
Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc.
Contains chapters written by a group of esteemed researchers in mathematical analysis
Includes problems and research questions in order to enhance understanding of the information provided
Offers references that help readers advance to further study
Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and ApplicationsSelected Topics includes the most recent research from a range of mathematical fields.
Michael Ruzhansky, Ph.D., is Professor in the Department of Mathematics at Imperial College London, UK. Dr. Ruzhansky was awarded the Ferran Sunyer I Balaguer Prize in 2014.
Hemen Dutta, Ph.D., is Senior Assistant Professor of Mathematics at Gauhati University, India.
Ravi P. Agarwal, Ph.D., is Professor and Chair of the Department of Mathematics at Texas A&M University-Kingsville, Kingsville, USA.
Описание: This Unique Volume Summarizes With A Historical Perspective Several Of The Major Scientific Achievements Of Ludwig Faddeev, With A Foreword By Nobel Laureate C N Yang. The Volume That Spans Over Fifty Years Of Faddeev'S Career Begins Where He Started His Own Scientific Research, In The Subject Of Scattering Theory And The Three-Body Problem. It Then Continues To Describe Faddeev'S Contributions To Automorphic Functions, Followed By An Extensive Account Of His Many Fundamental Contributions To Quantum Field Theory Including His Original Article On Ghosts With Popov. Faddeev'S Contributions To Soliton Theory And Integrable Models Are Then Described, Followed By A Survey Of His Work On Quantum Groups. The Final Scientific Section Is Devoted To Faddeev'S Contemporary Research Including Articles On His Long-Term Interest In Constructing Knotted Solitons And Understanding Confinement. The Volume Concludes With His Personal View On Science And Mathematical Physics In Particular.
Описание: Generalising Newton's law of gravitation, general relativity is one of the pillars of modern physics. While applications in the beginning were restricted to isolated effects such as a proper understanding of Mercury's orbit, the second half of the twentieth century saw a massive development of applications. These include cosmology, gravitational waves, and even very practical results for satellite based positioning systems as well as different approaches to unite general relativity with another very successful branch of physics – quantum theory. On the occassion of general relativity's centennial, leading scientists in the different branches of gravitational research review the history and recent advances in the main fields of applications of the theory, which was referred to by Lev Landau as “the most beautiful of the existing physical theories”. Contributions from: Andy C. Fabian, AnthonyL. Lasenby, Astrophysical black Holes Neil Ashby, GNSS and other applications of General Relativity Gene Byrd, Arthur Chernin, Pekka Teerikorpi, Mauri Vaaltonen,Observations of general Relativity at strong and weaks limits Ignazio Ciufolini, General Relativity and dragging of inertial frames Carlo Rovelli, The strange world of quantum spacetime
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