Lectures on Selected Topics in Mathematical Physics: Further Applications of Lie Theory, William A. Schwalm
Автор: Wazwaz Abdul-Majid Название: First Course In Integral Equations, A (Second Edition) ISBN: 9814675121 ISBN-13(EAN): 9789814675123 Издательство: World Scientific Publishing Рейтинг: Цена: 6336.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations.
Описание: This book is a sequel to Lectures on Selected Topics in Mathematical Physics: Introduction to Lie Theory with Applications . This volume is devoted mostly to Lie groups. Lie algebras and generating functions, both for standard special functions and for solution of certain types of physical problems. It is an informal treatment of these topics intended for physics graduate students or others with a physics background wanting a brief and informal introduction to the subjects addressed in a style and vocabulary not completely unfamiliar.
Описание: This book provides an introduction to Lie Theory for first year graduate students and professional physicists who may not have across the theory in their studies. In particular, it is a summary overview of the theory of finite groups, a brief description of a manifold, and then an informal development of the theory of one-parameter Lie groups, especially as they apply to ordinary differential equations. The treatment is informal, but systematic and reasonably self-contained, as it assumes a familiarity with basic physics and applied calculus, but it does not assume additional mathematical training. Interested readers should have a fair chance of finding symmetries of a second order differential equation and should be able to use it to reduce the order of the differential equation.
Автор: Watrous, John (university Of Waterloo, Ontario) Название: The theory of quantum information ISBN: 1107180562 ISBN-13(EAN): 9781107180567 Издательство: Cambridge Academ Рейтинг: Цена: 11563.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Intended for graduate students and researchers, this book presents a formal development of the mathematical theory of quantum information. Largely self-contained, with clear proofs and a wide range of exercises, it will help the reader grasp the fundamental facts and techniques that form the mathematical foundations of the subject.
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.
Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights.
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: 24392.00 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
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: 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
Описание: This is the second, amended edition of the book. In addition to the material of the first edition it contains a derivation of the value of action for each of those Harrington–Shepard calorons/anticalorons that are relevant for the emergence of the thermal ground state, discussions of the caloron center vs. its periphery, of the role of the thermal ground state in U(1) wave propagation, of photonic particle–wave duality, and of calculational intricacies and book-keeping related to one-loop scattering of massless modes in the deconfining phase of an SU(2) Yang–Mills theory. Moreover, a derivation of the temperature–redshift relation of the CMB in deconfining SU(2) Yang–Mills thermodynamics and its application to explaining an apparent early re-ionization of the Universe are given. Finally, a mechanism of mass generation for cosmic neutrinos is proposed.
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