Irreducible Tensor Methods

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Irreducible Tensor Methods

Author : Brian L. Silver
Publisher : Academic Press
ISBN 13 : 1483191818
Total Pages : 248 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Irreducible Tensor Methods by : Brian L. Silver

Download or read book Irreducible Tensor Methods written by Brian L. Silver and published by Academic Press. This book was released on 2013-09-17 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Irreducible Tensor Methods: An Introduction for Chemists explains the theory and application of irreducible tensor operators. The book discusses a compact formalism to describe the effect that results on an arbitrary function of a given set of coordinates when that set is subjected to a rotation about its origin. The text also explains the concept of irreducible tensor operators, particularly, as regards the transformation properties of operators under coordinate transformations, and, in a special way, the group of rotations. The book examines the systematic construction of compound tensor operators from simple operators to classify the behavior of any operator under coordinate rotations. This classification is a significant component of the irreducible tensor method. The text explains the use of the 6-j and 9-j symbols to complete theoretical concepts that are applied in irreducible tensor methods dealing with problems of atomic and molecular physics. The book describes the matrix elements in multielectron systems, as well as the reduced matrix elements found in these systems. The book is suitable for nuclear physicists, molecular physicists, scientists, and academicians in the field of quantum mechanics or advanced chemistry.

The Irreducible Tensor Method for Molecular Symmetry Groups

Author : J. S. Griffith
Publisher : Courier Dover Publications
ISBN 13 : 0486450473
Total Pages : 148 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis The Irreducible Tensor Method for Molecular Symmetry Groups by : J. S. Griffith

Download or read book The Irreducible Tensor Method for Molecular Symmetry Groups written by J. S. Griffith and published by Courier Dover Publications. This book was released on 2006-03-10 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduates and graduate students, this text covers V coefficients for the octahedral group and other symmetry groups, W coefficients, irreducible products and their matrix elements, two-electron formulae for the octahedral group, fractional parentage, X coefficients, spin, and matrices of one-electron operators. 1962 edition.

The Irreducible Tensor Method for Molecular Symmetry Groups

Author : John Stanley Griffith
Publisher :
ISBN 13 :
Total Pages : 134 pages
Book Rating : 4.:/5 (638 download)

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Book Synopsis The Irreducible Tensor Method for Molecular Symmetry Groups by : John Stanley Griffith

Download or read book The Irreducible Tensor Method for Molecular Symmetry Groups written by John Stanley Griffith and published by . This book was released on 2006 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Irreducible Cartesian Tensors

Author : Robert F. Snider
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110564866
Total Pages : 268 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Irreducible Cartesian Tensors by : Robert F. Snider

Download or read book Irreducible Cartesian Tensors written by Robert F. Snider and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-12-04 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers the concept of cartesian tensors with the needs and interests of physicists, chemists and other physical scientists in mind. After introducing elementary tensor operations and rotations, spherical tensors, combinations of tensors are introduced, also covering Clebsch-Gordan coefficients. After this, readers from the physical sciences will find generalizations of the results to spinors and applications to quantum mechanics.

Tensor Methods and a Unified Representation of Theory of SU3

Author : N. Mukunda
Publisher :
ISBN 13 :
Total Pages : 70 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Tensor Methods and a Unified Representation of Theory of SU3 by : N. Mukunda

Download or read book Tensor Methods and a Unified Representation of Theory of SU3 written by N. Mukunda and published by . This book was released on 1964 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tensor Methods in Statistics

Author : Peter McCullagh
Publisher : Courier Dover Publications
ISBN 13 : 0486832694
Total Pages : 308 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Tensor Methods in Statistics by : Peter McCullagh

Download or read book Tensor Methods in Statistics written by Peter McCullagh and published by Courier Dover Publications. This book was released on 2018-07-18 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.

Tensors for Physics

Author : Siegfried Hess
Publisher : Springer
ISBN 13 : 331912787X
Total Pages : 449 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Tensors for Physics by : Siegfried Hess

Download or read book Tensors for Physics written by Siegfried Hess and published by Springer. This book was released on 2015-04-25 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.

Irreducible Tensorial Sets

Author :
Publisher :
ISBN 13 :
Total Pages : 171 pages
Book Rating : 4.:/5 (58 download)

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Book Synopsis Irreducible Tensorial Sets by :

Download or read book Irreducible Tensorial Sets written by and published by . This book was released on 1959 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Tensor Analysis

Author : Liqun Qi
Publisher : SIAM
ISBN 13 : 1611974747
Total Pages : 313 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Tensor Analysis by : Liqun Qi

Download or read book Tensor Analysis written by Liqun Qi and published by SIAM. This book was released on 2017-04-19 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors. ?

Tensor Network Contractions

Author : Shi-Ju Ran
Publisher : Springer Nature
ISBN 13 : 3030344894
Total Pages : 160 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Group Theoretical Methods in Physics

Author : Robert Shar
Publisher : Elsevier
ISBN 13 : 0323141528
Total Pages : 685 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Group Theoretical Methods in Physics by : Robert Shar

Download or read book Group Theoretical Methods in Physics written by Robert Shar and published by Elsevier. This book was released on 2012-12-02 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Theoretical Methods in Physics: Proceedings of the Fifth International Colloquium provides information pertinent to the fundamental aspects of group theoretical methods in physics. This book provides a variety of topics, including nuclear collective motion, complex Riemannian geometry, quantum mechanics, and relativistic symmetry. Organized into six parts encompassing 64 chapters, this book begins with an overview of the theories of nuclear quadrupole dynamics. This text then examines the conventional approach in the determination of superstructures. Other chapters consider the Hamiltonian formalism and how it is applied to the KdV equation and to a slight variant of the KdV equation. This book discusses as well the significant differential equations of mathematical physics that are integrable Hamiltonian systems, including the equations governing self-induced transparency and the motion of particles under an inverse square potential. The final chapter deals with the decomposition of the tensor product of two irreducible representations of the symmetric group into a direct sum of irreducible representations. This book is a valuable resource for physicists.

Tensor Categories

Author : Pavel Etingof
Publisher : American Mathematical Soc.
ISBN 13 : 1470434415
Total Pages : 362 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Tensor Categories by : Pavel Etingof

Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.

Tensor Numerical Methods in Quantum Chemistry

Author : Venera Khoromskaia
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110391376
Total Pages : 343 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Tensor Numerical Methods in Quantum Chemistry by : Venera Khoromskaia

Download or read book Tensor Numerical Methods in Quantum Chemistry written by Venera Khoromskaia and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conventional numerical methods when applied to multidimensional problems suffer from the so-called "curse of dimensionality", that cannot be eliminated by using parallel architectures and high performance computing. The novel tensor numerical methods are based on a "smart" rank-structured tensor representation of the multivariate functions and operators discretized on Cartesian grids thus reducing solution of the multidimensional integral-differential equations to 1D calculations. We explain basic tensor formats and algorithms and show how the orthogonal Tucker tensor decomposition originating from chemometrics made a revolution in numerical analysis, relying on rigorous results from approximation theory. Benefits of tensor approach are demonstrated in ab-initio electronic structure calculations. Computation of the 3D convolution integrals for functions with multiple singularities is replaced by a sequence of 1D operations, thus enabling accurate MATLAB calculations on a laptop using 3D uniform tensor grids of the size up to 1015. Fast tensor-based Hartree-Fock solver, incorporating the grid-based low-rank factorization of the two-electron integrals, serves as a prerequisite for economical calculation of the excitation energies of molecules. Tensor approach suggests efficient grid-based numerical treatment of the long-range electrostatic potentials on large 3D finite lattices with defects.The novel range-separated tensor format applies to interaction potentials of multi-particle systems of general type opening the new prospects for tensor methods in scientific computing. This research monograph presenting the modern tensor techniques applied to problems in quantum chemistry may be interesting for a wide audience of students and scientists working in computational chemistry, material science and scientific computing.

Molecular Structure and Statistical Thermodynamics

Author : Kenneth S. Pitzer
Publisher : World Scientific
ISBN 13 : 9812795960
Total Pages : 537 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Molecular Structure and Statistical Thermodynamics by : Kenneth S. Pitzer

Download or read book Molecular Structure and Statistical Thermodynamics written by Kenneth S. Pitzer and published by World Scientific. This book was released on 1993 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers molecular structural information, statistical methods and thermodynamic measurements, and the ways in which the relative role of each differs from another. By putting together selected papers in a single publication, the book highlights the cohesive aspects of certain advances through time and development, and can aid historical studies. Several papers from journals not widely circulated can also be found in this selection of papers.

An Introduction to Tensors and Group Theory for Physicists

Author : Nadir Jeevanjee
Publisher : Birkhäuser
ISBN 13 : 3319147943
Total Pages : 317 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis An Introduction to Tensors and Group Theory for Physicists by : Nadir Jeevanjee

Download or read book An Introduction to Tensors and Group Theory for Physicists written by Nadir Jeevanjee and published by Birkhäuser. This book was released on 2015-03-11 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this highly praised textbook provides an introduction to tensors, group theory, and their applications in classical and quantum physics. Both intuitive and rigorous, it aims to demystify tensors by giving the slightly more abstract but conceptually much clearer definition found in the math literature, and then connects this formulation to the component formalism of physics calculations. New pedagogical features, such as new illustrations, tables, and boxed sections, as well as additional “invitation” sections that provide accessible introductions to new material, offer increased visual engagement, clarity, and motivation for students. Part I begins with linear algebraic foundations, follows with the modern component-free definition of tensors, and concludes with applications to physics through the use of tensor products. Part II introduces group theory, including abstract groups and Lie groups and their associated Lie algebras, then intertwines this material with that of Part I by introducing representation theory. Examples and exercises are provided in each chapter for good practice in applying the presented material and techniques. Prerequisites for this text include the standard lower-division mathematics and physics courses, though extensive references are provided for the motivated student who has not yet had these. Advanced undergraduate and beginning graduate students in physics and applied mathematics will find this textbook to be a clear, concise, and engaging introduction to tensors and groups. Reviews of the First Edition “[P]hysicist Nadir Jeevanjee has produced a masterly book that will help other physicists understand those subjects [tensors and groups] as mathematicians understand them... From the first pages, Jeevanjee shows amazing skill in finding fresh, compelling words to bring forward the insight that animates the modern mathematical view...[W]ith compelling force and clarity, he provides many carefully worked-out examples and well-chosen specific problems... Jeevanjee’s clear and forceful writing presents familiar cases with a freshness that will draw in and reassure even a fearful student. [This] is a masterpiece of exposition and explanation that would win credit for even a seasoned author.” —Physics Today "Jeevanjee’s [text] is a valuable piece of work on several counts, including its express pedagogical service rendered to fledgling physicists and the fact that it does indeed give pure mathematicians a way to come to terms with what physicists are saying with the same words we use, but with an ostensibly different meaning. The book is very easy to read, very user-friendly, full of examples...and exercises, and will do the job the author wants it to do with style.” —MAA Reviews

Density Matrix Theory and Applications

Author : Karl Blum
Publisher : Springer Science & Business Media
ISBN 13 : 1461568080
Total Pages : 217 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Density Matrix Theory and Applications by : Karl Blum

Download or read book Density Matrix Theory and Applications written by Karl Blum and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics has been mostly concerned with those states of systems that are represented by state vectors. In many cases, however, the system of interest is incompletely determined; for example, it may have no more than a certain probability of being in the precisely defined dynamical state characterized by a state vector. Because of this incomplete knowledge, a need for statistical averaging arises in the same sense as in classical physics. The density matrix was introduced by J. von Neumann in 1927 to describe statistical concepts in quantum mechanics. The main virtue of the density matrix is its analytical power in the construction of general formulas and in the proof of general theorems. The evaluation of averages and probabilities of the physical quantities characterizing a given system is extremely cumbersome without the use of density matrix techniques. The representation of quantum mechanical states by density matrices enables the maximum information available on the system to be expressed in a compact manner and hence avoids the introduction of unnecessary vari ables. The use of density matrix methods also has the advantage of providing a uniform treatment of all quantum mechanical states, whether they are completely or incom~'\etely known. Until recently the use of the density matrix method has been mainly restricted to statistical physics. In recent years, however, the application of the density matrix has been gaining more and more importance in many other fields of physics.

Tensors: Geometry and Applications

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821869078
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tensors: Geometry and Applications by : J. M. Landsberg

Download or read book Tensors: Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.