Download or read book Algebraic Methods in Physics written by Jiri Patera and published by Springer Science & Business Media. This book was released on 2001 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-Similarities and Invariant Densities for Model Sets.- Model Sets and Self-Similarities.- Averaging Operators and Invariant Densities.- Further Remarks.- Outlook.- References.- Symmetry Operations in the Brain: Music and Reasoning.- Trion Model.- Music Enhances Spatial-Temporal Reasoning.- References.- Lie Modules of Bounded Multiplicities.- Simple L Modules with Finite-Dimensional Weight Spaces.- Completely Pointed Modules.- Completely Pointed Modules Tensored with Finite-Dimensional Modules.- References.- Moving Frames and Coframes.- References.- The Fibonacci-Deformed Harmonic Oscillator.- About Strictly Increasing Sequences of Positive Numbers.- Quantum Algebra Associated with the Spectrum ? = xn.- The ?-Natural Spectrum.- The Fibonacci Deformation of Weyl Algebra.- Coherent States and Some Special Functions.- References.- Continuous and Discrete Linearizable Systems: The Riccati Saga.- Brief Review of the Continuous Gambier Equation.- Discrete Analog of the Gambier Equation, Revisited.- Discrete Projective and Matrix Riccati Equations.- Discrete Conformai Riccati Equations.- Conclusions and Outlook.- References.- Superintegrability on Two-Dimensional Complex Euclidean Space.- Potential V5.- Potential V6.- Potential V7.- References.- Hydrodynamic Systems and the Higher-Dimensional Laplace Transformations of Cartan Submanifolds.- Hydrodynamic Systems Rich in Conservation Laws.- Applications of the Higher-Dimensional Laplace Transformation to Hydrodynamic Systems that are Rich in Conservation Laws.- References.- Branching Rules and Weight Multiplicities for Simple and Affine Lie Algebras.- Simple and Affine Lie Algebras.- Branching Rules for Simple Lie Algebras.- Young Diagrams and Branching Rules.- Weight Multiplicities of Simple Lie Algebras.- Young Tableaux and Weight Multiplicities.- Branching Rule Multiplicities for the Restriction from Affine to Simple Lie Algebras.- Branching Rules Derived from Characters.- Weight Multiplicities of Affine Lie Algebras.- References.- Conditions for the Existence of Higher Symmetries and Nonlinear Evolutionary Equations on the Lattice.- Construction of the Classifying Conditions.- The Toda Lattice Class.- References.- Complete Description of the Voronoï Cell of the Lie Algebra An Weight Lattice. On the Bounds for the Number of d-Faces of the n-Dimensional Voronoï Cells.- The Expression of the Bounds Nd(n) Obtained by Voronoï.- Detailed Description of the Voronoï Cells of the A(TM) Lattices.- The New Explicit Expression of Bounds Nd(n).- Expression of Nd(n) as Multiple of a Stirling Number of Second Kind.- Final Remarks.- References.- The Relativistic Oscillator and the Mass Spectra of Baryons.- The System of Three Relativistic Scalar Particles with Oscillator Interactions.- An Approach to the Spinorial Relativistic Three-Body System.- References.- Seiberg-Witten Theory Without Tears.- N = 2 Supersymmetry.- N = 2 Superaction.- Textbook Properties.- Spontaneous Symmetry-Breaking.- Holomorphy and Duality.- Perturbative and Nonperturbative F (A).- Preliminaries.- Fuchsian Maps.- The Schwarzian Derivatives.- SW Choice.- Correctness.- Uniqueness.- References.- Bargmann Representation for Some Deformed Harmonic Oscillators with Non-Fock Representation.- Representations.- Toward a Bargmann Representation.- The "q-Oscillator".- Generalization of the Previous Example.- Deformed Algebra Associated to a Given Weight function.- Bargmann Representations Corresponding to Different ?.- The Case of an Annulus.- Conclusion.- References.- The Vector-Coherent-State Inducing Construction for Clebsch-Gordan Coefficients.- Induced Representations of su(4).- SU(4) Clebsch-Gordan Coefficients.- Summary.- References.- Highest-Weight Representations of Borcherds Algebras.- Borcherds Algebras.- Cartan Subalgebra of an Affine Kac-Moody Algebra.- Adding Energy and Number Operators to the Cartan Subalgebra.- Conclusions.- References.- Graded Contractions of Lie Algebras of Physical Interest.- Notion of Graded
Download or read book Algebraic Methods in Physics written by Yvan Saint-Aubin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Methods in Statistical Mechanics and Quantum Field Theory written by Dr. Gérard G. Emch and published by Courier Corporation. This book was released on 2014-08-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Methods in Quantum Chemistry and Physics written by Francisco M. Fernandez and published by CRC Press. This book was released on 1995-10-24 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic Methods in Quantum Chemistry and Physics written by Francisco M. Fernandez and published by CRC Press. This book was released on 2020-01-16 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebraic and Diagrammatic Methods in Many Fermion Theory written by Frank E. Harris and published by Courier Dover Publications. This book was released on 2020-01-15 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on the use of electron correlation effects in the description of the electronic structure of atoms, molecules, and crystals is intended for graduate students in physical chemistry and physics. Modern theories of electronic structure and methods of incorporating electron correlation contributions are developed using a diagrammatic and algebraic formulation, and the methods developed in the text are illustrated with examples from molecular and solid state quantum mechanics. A brief Introduction is followed by chapters on operator algebra, the independent-particle model, occupation-number formalism, and diagrams. Additional topics include the configuration-interaction method, the many-body perturbation theory, and the coupled-cluster method.
Download or read book Algebraic Methods in Nonlinear Perturbation Theory written by V.N. Bogaevski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Of interest to everybody working on perturbation theory in differential equations, this book requires only a standard mathematical background in engineering and does not require reference to the special literature. Topics covered include: matrix perturbation theory; systems of ordinary differential equations with small parameters; reconstruction and equations in partial derivatives. While boundary problems are not discussed, the book is clearly illustrated by numerous examples.
Download or read book Geometric and Algebraic Topological Methods in Quantum Mechanics written by G. Giachetta and published by World Scientific. This book was released on 2005 with total page 715 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry''s geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.
Download or read book Mathematical Methods of Classical Mechanics written by V.I. Arnol'd and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Download or read book Mathematical Methods in Quantum Mechanics written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2009 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the theory of operators on Hilbert space have been deeply linked since their beginnings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduction to the mathematical methods of quantum mechanics, with a view towards applications to Schrodinger operators. Part 1 of the book is a concise introduction to the spectral theory of unbounded operators. Only those topics that will be needed for later applications are covered. The spectral theorem is a central topic in this approach and is introduced at an early stage. Part 2 starts with the free Schrodinger equation and computes the free resolvent and time evolution. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the nondegeneracy of the ground state, spectra of atoms, and scattering theory. This book serves as a self-contained introduction to spectral theory of unbounded operators in Hilbert space with full proofs and minimal prerequisites: Only a solid knowledge of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional analysis and no Lebesgue integration theory are assumed. It develops the mathematical tools necessary to prove some key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended for beginning graduate students in both mathematics and physics and provides a solid foundation for reading more advanced books and current research literature. It is well suited for self-study and includes numerous exercises (many with hints).
Download or read book Algebraic and Geometric Methods in Mathematical Physics written by Anne Boutet de Monvel and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
Download or read book Topological and Algebraic Methods in Contemporary Mathematical Physics written by B. A. Dubrovin and published by . This book was released on 2003 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Methods of Applied Mathematics written by Francis B. Hildebrand and published by Courier Corporation. This book was released on 2012-06-08 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.
Download or read book Mathematics of Classical and Quantum Physics written by Frederick W. Byron and published by Courier Corporation. This book was released on 2012-04-26 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.
Download or read book General Algebraic Methods in Mathematics and Physics written by Hans Schwerdtfeger and published by . This book was released on 1949 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mirror Symmetry written by Kentaro Hori and published by American Mathematical Soc.. This book was released on 2003 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough and detailed exposition is the result of an intensive month-long course on mirror symmetry sponsored by the Clay Mathematics Institute. It develops mirror symmetry from both mathematical and physical perspectives with the aim of furthering interaction between the two fields. The material will be particularly useful for mathematicians and physicists who wish to advance their understanding across both disciplines. Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differential equations obtained from a ``mirror'' geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar-Vafa invariants. This book gives a single, cohesive treatment of mirror symmetry. Parts 1 and 2 develop the necessary mathematical and physical background from ``scratch''. The treatment is focused, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a ``pairing'' of geometries. The proof involves applying $R\leftrightarrow 1/R$ circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic setting, beginning with the moduli spaces of curves and maps, and uses localization techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry. Part 5 is devoted to advanced topi This one-of-a-kind book is suitable for graduate students and research mathematicians interested in mathematics and mathematical and theoretical physics.
Download or read book Algebraic Methods in Operator Theory written by Raul E. Curto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of operators stands at the intersection of the frontiers of modern analysis and its classical counterparts; of algebra and quantum mechanics; of spectral theory and partial differential equations; of the modern global approach to topology and geometry; of representation theory and harmonic analysis; and of dynamical systems and mathematical physics. The present collection of papers represents contributions to a conference, and they have been carefully selected with a view to bridging different but related areas of mathematics which have only recently displayed an unexpected network of interconnections, as well as new and exciting cross-fertilizations. Our unify ing theme is the algebraic view and approach to the study of operators and their applications. The complementarity between the diversity of topics on the one hand and the unity of ideas on the other has been stressed. Some of the longer contributions represent material from lectures (in expanded form and with proofs for the most part). However, the shorter papers, as well as the longer ones, are an integral part of the picture; they have all been carefully refereed and revised with a view to a unity of purpose, timeliness, readability, and broad appeal. Raul Curto and Paile E. T.
