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Author: James D. Louck
Publisher: World Scientific
ISBN: 9812814728
Category : Science
Languages : en
Pages : 642
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Book Description
Notation -- Quantum angular momentum -- Composite systems -- Graphs and adjacency diagrams -- Generating functions -- The D[lambda] polynomials: form -- Operator actions in Hilbert space -- The D[lambda] polynomials: structure -- The general linear and unitary groups -- Tensor operator theory -- Compendium A. Basic algebraic objects -- Compendium B. Combinatorial objects.
Author: James D. Louck
Publisher: World Scientific
ISBN: 9812814728
Category : Science
Languages : en
Pages : 642
Get Book Here
Book Description
Notation -- Quantum angular momentum -- Composite systems -- Graphs and adjacency diagrams -- Generating functions -- The D[lambda] polynomials: form -- Operator actions in Hilbert space -- The D[lambda] polynomials: structure -- The general linear and unitary groups -- Tensor operator theory -- Compendium A. Basic algebraic objects -- Compendium B. Combinatorial objects.
Author: James D Louck
Publisher: World Scientific
ISBN: 9814458732
Category : Mathematics
Languages : en
Pages : 381
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Book Description
This monograph is a synthesis of the theory of the pairwise coupling of the angular momenta of arbitrarily many independent systems to the total angular momentum in which the universal role of doubly stochastic matrices and their quantum-mechanical probabilistic interpretation is a major theme. A uniform viewpoint is presented based on the structure of binary trees. This includes a systematic method for the evaluation of all 3n-j coefficients and their relationship to cubic graphs. A number of topical subjects that emerge naturally are also developed, such as the algebra of permutation matrices, the properties of magic squares and an associated generalized Regge form, the Zeilberger counting formula for alternating sign matrices, and the Heisenberg ring problem, viewed as a composite system in which the total angular momentum is conserved.The readership is intended to be advanced graduate students and researchers interested in learning about the relationship between unitary symmetry and combinatorics and challenging unsolved problems. The many examples serve partially as exercises, but this monograph is not a textbook. It is hoped that the topics presented promote further and more rigorous developments that lead to a deeper understanding of the angular momentum properties of complex systems viewed as composite wholes.
Author: James D Louck
Publisher: World Scientific
ISBN: 9814470961
Category : Science
Languages : en
Pages : 642
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Book Description
This monograph integrates unitary symmetry and combinatorics, showing in great detail how the coupling of angular momenta in quantum mechanics is related to binary trees, trivalent trees, cubic graphs, MacMahon's master theorem, and other basic combinatorial concepts. A comprehensive theory of recoupling matrices for quantum angular momentum is developed. For the general unitary group, polynomial forms in many variables called matrix Schur functions have the remarkable property of giving all irreducible representations of the general unitary group and are the basic objects of study. The structure of these irreducible polynomials and the reduction of their Kronecker product is developed in detail, as is the theory of tensor operators.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
From 1967 to 1994, Larry Biedenham and I collaborated on 35 papers on various aspects of the general unitary group, especially its unitary irreducible representations and Wigner-Clebsch-Gordan coefficients. In our studies to unveil comprehensible structures in this subject, we discovered several nice results in special functions and combinatorics. The more important of these will be presented and their present status reviewed.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 13
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Book Description
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.
Author: Roger Howe
Publisher: Springer
ISBN: 1493915908
Category : Mathematics
Languages : en
Pages : 562
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Book Description
Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.
Author: Tadeusz Lulek
Publisher: World Scientific
ISBN: 9814543632
Category :
Languages : en
Pages : 494
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Book Description
This volume continues the series of proceedings of summer schools on theoretical physics which aim at an adequate description of the structure of condensed matter in terms of sophisticated, advanced mathematical tools. This time, the main emphasis is put on the question of whether (and when) the energy bands in solids are continuous. Profs. L Michel, J Zak and others consider the origin, existence and continuity of band structure. Also, some previously discussed problems (magnetic symmetry, flux quantization, statistics, quasicrystals, the Bethe ansatz) are pursued further, and appropriate mathematical tools, rooted in “actions of groups on sets”, are developed.
Author: J. Schechter
Publisher:
ISBN:
Category : Eightfold way (Nuclear physics)
Languages : en
Pages : 38
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Book Description
Author: Eric S. Egge
Publisher: American Mathematical Soc.
ISBN: 1470448998
Category : Education
Languages : en
Pages : 342
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Book Description
This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneous, and Schur function bases; the skew Schur functions; the Jacobi–Trudi identities; the involution ω ω; the Hall inner product; Cauchy's formula; the RSK correspondence and how to implement it with both insertion and growth diagrams; the Pieri rules; the Murnaghan–Nakayama rule; Knuth equivalence; jeu de taquin; and the Littlewood–Richardson rule. The book also includes glimpses of recent developments and active areas of research, including Grothendieck polynomials, dual stable Grothendieck polynomials, Stanley's chromatic symmetric function, and Stanley's chromatic tree conjecture. Written in a conversational style, the book contains many motivating and illustrative examples. Whenever possible it takes a combinatorial approach, using bijections, involutions, and combinatorial ideas to prove algebraic results. The prerequisites for this book are minimal—familiarity with linear algebra, partitions, and generating functions is all one needs to get started. This makes the book accessible to a wide array of undergraduates interested in combinatorics.
Author: Melvyn B. Nathanson
Publisher: Springer Nature
ISBN: 3030679969
Category : Mathematics
Languages : en
Pages : 445
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Book Description
This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.
