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Coherent Transform Quantization And Poisson Geometry
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Book Synopsis Coherent Transform, Quantization and Poisson Geometry by : Mikhail Vladimirovich Karasev
Download or read book Coherent Transform, Quantization and Poisson Geometry written by Mikhail Vladimirovich Karasev and published by American Mathematical Soc.. This book was released on 1998 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume copntains three extensive articles written by Karasev and his pupils. Topics covered include the following: coherent states and irreducible representations for algebras with non-Lie permutation relations, Hamilton dynamics and quantization over stable isotropic submanifolds, and infinitesimal tensor complexes over degenerate symplectic leaves in Poisson manifolds. The articles contain many examples (including from physics) and complete proofs.
Book Synopsis Quantum Algebras and Poisson Geometry in Mathematical Physics by : Mikhail Vladimirovich Karasev
Download or read book Quantum Algebras and Poisson Geometry in Mathematical Physics written by Mikhail Vladimirovich Karasev and published by American Mathematical Soc.. This book was released on 2005 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents applications of Poisson geometry to some fundamental well-known problems in mathematical physics. This volume is suitable for graduate students and researchers interested in mathematical physics. It uses methods such as: unexpected algebras with non-Lie commutation relations, dynamical systems theory, and semiclassical asymptotics.
Book Synopsis From Geometry to Quantum Mechanics by : Yoshiaki Maeda
Download or read book From Geometry to Quantum Mechanics written by Yoshiaki Maeda and published by Springer Science & Business Media. This book was released on 2007-04-22 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Invited articles in differential geometry and mathematical physics in honor of Hideki Omori * Focus on recent trends and future directions in symplectic and Poisson geometry, global analysis, Lie group theory, quantizations and noncommutative geometry, as well as applications of PDEs and variational methods to geometry * Will appeal to graduate students in mathematics and quantum mechanics; also a reference
Book Synopsis Asymptotic Methods for Wave and Quantum Problems by : M. V. Karasev
Download or read book Asymptotic Methods for Wave and Quantum Problems written by M. V. Karasev and published by American Mathematical Soc.. This book was released on 2003 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.
Book Synopsis Lectures on Poisson Geometry by : Marius Crainic
Download or read book Lectures on Poisson Geometry written by Marius Crainic and published by American Mathematical Soc.. This book was released on 2021-09-14 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way. —Alan Weinstein, University of California at Berkeley This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study. —Eckhard Meinrenken, University of Toronto
Book Synopsis Geometric Models for Noncommutative Algebras by : Ana Cannas da Silva
Download or read book Geometric Models for Noncommutative Algebras written by Ana Cannas da Silva and published by American Mathematical Soc.. This book was released on 1999 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is based on a course, ``Geometric Models for Noncommutative Algebras'' taught by Professor Weinstein at Berkeley. Noncommutative geometry is the study of noncommutative algebras as if they were algebras of functions on spaces, for example, the commutative algebras associated to affine algebraic varieties, differentiable manifolds, topological spaces, and measure spaces. In this work, the authors discuss several types of geometric objects (in the usual sense of sets with structure) that are closely related to noncommutative algebras. Central to the discussion are symplectic and Poisson manifolds, which arise when noncommutative algebras are obtained by deforming commutative algebras. The authors also give a detailed study of groupoids (whose role in noncommutative geometry has been stressed by Connes) as well as of Lie algebroids, the infinitesimal approximations to differentiable groupoids. Featured are many interesting examples, applications, and exercises. The book starts with basic definitions and builds to (still) open questions. It is suitable for use as a graduate text. An extensive bibliography and index are included.
Book Synopsis Geometry, Topology, and Mathematical Physics by : V. M. Buchstaber
Download or read book Geometry, Topology, and Mathematical Physics written by V. M. Buchstaber and published by American Mathematical Soc.. This book was released on 2008-01-01 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers based on presentations given in 2006-2007 at the S. P. Novikov Seminar at the Steklov Mathematical Institute in Moscow. Novikov's diverse interests are reflected in the topics presented in the book. The articles address topics in geometry, topology, and mathematical physics. The volume is suitable for graduate students and researchers interested in the corresponding areas of mathematics and physics.
Book Synopsis Commuting Elements in Q-Deformed Heisenberg Algebras by : Lars Hellström
Download or read book Commuting Elements in Q-Deformed Heisenberg Algebras written by Lars Hellström and published by World Scientific. This book was released on 2000-09-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative algebras, rings and other noncommutative objects, along with their more classical commutative counterparts, have become a key part of modern mathematics, physics and many other fields. The q-deformed Heisenberg algebras defined by deformed Heisenberg canonical commutation relations of quantum mechanics play a distinguished role as important objects in pure mathematics and in many applications in physics. The structure of commuting elements in an algebra is of fundamental importance for its structure and representation theory as well as for its applications. The main objects studied in this monograph are q-deformed Heisenberg algebras — more specifically, commuting elements in q-deformed Heisenberg algebras. In this book the structure of commuting elements in q-deformed Heisenberg algebras is studied in a systematic way. Many new results are presented with complete proofs. Several appendices with some general theory used in other parts of the book include material on the Diamond lemma for ring theory, a theory of degree functions in arbitrary associative algebras, and some basic facts about q-combinatorial functions over an arbitrary field. The bibliography contains, in addition to references on q-deformed Heisenberg algebras, some selected references on related subjects and on existing and potential applications. The book is self-contained, as far as proofs and the background material are concerned. In addition to research and reference purposes, it can be used in a special course or a series of lectures on the subject or as complementary material to a general course on algebra. Specialists as well as doctoral and advanced undergraduate students in mathematics and physics will find this book useful in their research and study. Contents:Immediate Consequences of the Commutation RelationsBases and Normal Form in H(q) and H(q,J)Degree in and Gradation of H(q,J)Centralisers of Elements in H(q,J)Centralisers of Elements in H(q)Algebraic Dependence of Commuting Elements in H(q) and H(q,J)Representations of H(q,J) by q-Difference OperatorsThe Diamond LemmaDegree Functions and Gradationsq-Special Combinatorics Readership: Researchers, graduate students and undergraduates in algebra and physics. Keywords:q-Deformed Heisenberg Algebras;Normal Form;Gradation;Commuting Elements;q-Difference Operators;Centraliser;Diamond Lemma;Graded Algebras;q-CombinatoricsReviews:“The exposition is very detailed and the book may serve both as a text for researchers interested in the theory of quantum deformations and as an introductory text for beginners.”Mathematical Reviews “The book has an extended list of references (410 items). The exposition is self-contained and may be very useful both to specialists and doctoral or advanced undergraduate students.”Romanian Journal of Pure and Applied Mathematics “… this is a very elementary and full of detail book, which some beginners in the theory of quantum deformations can find interesting and useful to dip into for calculations or to learn about the Diamond Lemma, gradation or q-calculus.”Mathematics Abstracts
Book Synopsis Nonlinear Equations and Spectral Theory by : M. S. Birman
Download or read book Nonlinear Equations and Spectral Theory written by M. S. Birman and published by American Mathematical Soc.. This book was released on 2007 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Translations of articles on mathematics appearing in various Russian mathematical serials.
Book Synopsis Moscow Seminar on Mathematical Physics, II by : Yu. A. Neretin
Download or read book Moscow Seminar on Mathematical Physics, II written by Yu. A. Neretin and published by American Mathematical Soc.. This book was released on 2008 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Theoretical and Experimental Physics (ITEP) is internationally recognized for achievements in various branches of theoretical physics. For many years, the seminars at ITEP have been among the main centers of scientific life in Moscow. This volume is a collection of articles by participants of the seminar on mathematical physics that has been held at ITEP since 1983. This is the second such collection; the first was published in the same series, AMS Translations, Series 2, vol. 191. The papers in the volume are devoted to several mathematical topics that strongly influenced modern theoretical physics. Among these topics are cohomology and representations of infinite Lie algebras and superalgebras, Hitchin and Knizhnik-Zamolodchikov-Bernard systems, and the theory of $D$-modules. The book is intended for graduate students and research mathematicians working in algebraic geometry, representation theory, and mathematical physics.
Book Synopsis Northern California Symplectic Geometry Seminar by : Y. Eliashberg
Download or read book Northern California Symplectic Geometry Seminar written by Y. Eliashberg and published by American Mathematical Soc.. This book was released on 1999 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 12 papers are from various meeting of the seminar, which has met regularly since 1989. They discuss the quantization of symplectic orbitfolds and group actions; Hamiltonian dynamical systems without period orbits; the stabilization of symplectic inequalities and applications; Engel deformations and contact structures; quantum products for mapping tori and the Atiya-Floer conjecture; the cohomology rings of Hamiltonian T-spaces; symmetric spaces, Kahler geometry, and Hamiltonian dynamics; the mirror formula for quintic threefolds; the virtual moduli cycle; Floer homology, Novikov rings, and complete intersections; surgery, quantum cohomology, and birational geometry; and group symplectic automorphisms. They are not indexed. Annotation copyrighted by Book News, Inc., Portland, OR.
Book Synopsis Topology, Ergodic Theory, Real Algebraic Geometry by : Vladimir G. Turaev
Download or read book Topology, Ergodic Theory, Real Algebraic Geometry written by Vladimir G. Turaev and published by American Mathematical Soc.. This book was released on 2001 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the memory of the Russian mathematician, V.A. Rokhlin (1919-1984). It is a collection of research papers written by his former students and followers, who are now experts in their fields. The topics in this volume include topology (the Morse-Novikov theory, spin bordisms in dimension 6, and skein modules of links), real algebraic geometry (real algebraic curves, plane algebraic surfaces, algebraic links, and complex orientations), dynamics (ergodicity, amenability, and random bundle transformations), geometry of Riemannian manifolds, theory of Teichmuller spaces, measure theory, etc. The book also includes a biography of Rokhlin by Vershik and two articles which should prove of historical interest.
Book Synopsis Proceedings of the St. Petersburg Mathematical Society Volume IV by : Olʹga Aleksandrovna Ladyzhenskai͡a
Download or read book Proceedings of the St. Petersburg Mathematical Society Volume IV written by Olʹga Aleksandrovna Ladyzhenskai͡a and published by American Mathematical Soc.. This book was released on 1999 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 11 papers are devoted to analysis, probability, and applications. The topics include the limit distribution of a homogeneous polynomial on the unit sphere of large dimensions, a survey of measures on abelian groups, the extension of analytic solutions of linear partial differential equations, asymptotics of the spectrum for two model problems in the theory of liquid vibrations, and countable analogues of pseudo-compact and Stone-Cech extensions. One offering is a biographical sketch of Julian Vasil'evich Sochotskii (1842-1927). No index. Member prices are $92 for institutions and $69 for individuals. Annotation copyrighted by Book News, Inc., Portland, OR.
Book Synopsis Lie Groups and Invariant Theory by : Ėrnest Borisovich Vinberg
Download or read book Lie Groups and Invariant Theory written by Ėrnest Borisovich Vinberg and published by American Mathematical Soc.. This book was released on 2005 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, devoted to the 70th birthday of A. L. Onishchik, contains a collection of articles by participants in the Moscow Seminar on Lie Groups and Invariant Theory headed by E. B. Vinberg and A. L. Onishchik. The book is suitable for graduate students and researchers interested in Lie groups and related topics.
Book Synopsis Operator Theory and Its Applications by : Michael Levitin
Download or read book Operator Theory and Its Applications written by Michael Levitin and published by American Mathematical Soc.. This book was released on 2010 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to the theory of linear operators in Hilbert spaces and its applications, the subjects covered in this book range from the abstract theory of Toeplitz operators to the analysis of very specific differential operators arising in quantum mechanics, electromagnetism, and the theory of elasticity.
Book Synopsis Model Theory and Applications by : O.V. Belegradek
Download or read book Model Theory and Applications written by O.V. Belegradek and published by American Mathematical Soc.. This book was released on 1999 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists. The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.
Book Synopsis Proceedings of the St. Petersburg Mathematical Society, Volume XIV by : Sankt-Peterburgskoe matematicheskoe obshchestvo
Download or read book Proceedings of the St. Petersburg Mathematical Society, Volume XIV written by Sankt-Peterburgskoe matematicheskoe obshchestvo and published by American Mathematical Soc.. This book was released on 2009 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains articles on analysis, probability, partial differential operators, frames, and other areas of mathematics. This volume also contains a comprehensive article about the classification of pseudo-regular convex polyhedra. It is suitable for a broad group of graduate students and researchers interested in the topics presented here.
