Applications Of Unitary Symmetry And Combinatorics

Applications of Unitary Symmetry and Combinatorics PDF
Author: James D. Louck
Publisher: World Scientific
ISBN: 9814350710
Size: 69.24 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 344
View: 7031

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Applications Of Unitary Symmetry And Combinatorics

by James D. Louck, Applications Of Unitary Symmetry And Combinatorics Books available in PDF, EPUB, Mobi Format. Download Applications Of Unitary Symmetry And Combinatorics books, 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.


Unitary Symmetry And Combinatorics

Unitary Symmetry And Combinatorics PDF
Author: James D Louck
Publisher: World Scientific
ISBN: 9814470961
Size: 74.11 MB
Format: PDF, ePub, Mobi
Category : Science
Languages : en
Pages : 644
View: 2529

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Unitary Symmetry And Combinatorics

by James D Louck, Unitary Symmetry And Combinatorics Books available in PDF, EPUB, Mobi Format. Download Unitary Symmetry And Combinatorics books, 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.


Algebraic Combinatorics On Words

Algebraic Combinatorics on Words PDF
Author: M. Lothaire
Publisher: Cambridge University Press
ISBN: 9780521812207
Size: 54.38 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 504
View: 2248

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Algebraic Combinatorics On Words

by M. Lothaire, Algebraic Combinatorics On Words Books available in PDF, EPUB, Mobi Format. Download Algebraic Combinatorics On Words books, Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.


Symmetry Representation Theory And Its Applications

Symmetry  Representation Theory and Its Applications PDF
Author: Roger Howe
Publisher: Springer
ISBN: 1493915908
Size: 80.61 MB
Format: PDF, Mobi
Category : Mathematics
Languages : en
Pages : 538
View: 6743

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Symmetry Representation Theory And Its Applications

by Roger Howe, Symmetry Representation Theory And Its Applications Books available in PDF, EPUB, Mobi Format. Download Symmetry Representation Theory And Its Applications books, 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.


Combinatorics And Applications

Combinatorics and Applications PDF
Author: K. S. Vijayan
Publisher:
ISBN:
Size: 69.58 MB
Format: PDF, ePub
Category : Combinatorial analysis
Languages : en
Pages : 389
View: 3825

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Combinatorics And Applications

by K. S. Vijayan, Combinatorics And Applications Books available in PDF, EPUB, Mobi Format. Download Combinatorics And Applications books,


Applications Of Random Matrices In Physics

Applications of Random Matrices in Physics PDF
Author: Édouard Brezin
Publisher: Springer Science & Business Media
ISBN: 140204531X
Size: 76.48 MB
Format: PDF, Docs
Category : Science
Languages : en
Pages : 510
View: 5695

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Applications Of Random Matrices In Physics

by Édouard Brezin, Applications Of Random Matrices In Physics Books available in PDF, EPUB, Mobi Format. Download Applications Of Random Matrices In Physics books, Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.


Asymptotic Combinatorics With Applications To Mathematical Physics

Asymptotic Combinatorics with Applications to Mathematical Physics PDF
Author: SPRINGER
Publisher: Springer Science & Business Media
ISBN: 3540403124
Size: 48.54 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 245
View: 3549

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Asymptotic Combinatorics With Applications To Mathematical Physics

by SPRINGER, Asymptotic Combinatorics With Applications To Mathematical Physics Books available in PDF, EPUB, Mobi Format. Download Asymptotic Combinatorics With Applications To Mathematical Physics books, At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.


The Mathematics Of The Periodic Table

The Mathematics of the Periodic Table PDF
Author: D. H. Rouvray
Publisher: Nova Science Pub Incorporated
ISBN:
Size: 16.70 MB
Format: PDF
Category : Science
Languages : en
Pages : 318
View: 6389

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The Mathematics Of The Periodic Table

by D. H. Rouvray, The Mathematics Of The Periodic Table Books available in PDF, EPUB, Mobi Format. Download The Mathematics Of The Periodic Table books, The Periodic Table effectively embraces the whole realm of chemistry within the confines of one comparatively simple and easily understood chart of the chemical elements. Over many years the Periodic Table has proven to be indispensable not only to chemists of all kinds but also to a host of other scientists, including biologists, geologists and physicists. It is thus hardly surprising that the Periodic Table has become one of our most celebrated contemporary scientific icons. In the present work various aspects of the Periodic Table that are seldom if ever featured elsewhere are given prominence. The twelve presentations contained herein all have a mathematical flavour because it is the intention to highlight the often-neglected mathematical features of the Periodic Table and several closely related topics. The book starts out by considering predictions of what the ultimate size of the Periodic Table will be when all of the possible artificial chemical elements have been synthesised. It then moves on to an examination of the nature of the periodicity extant in the Periodic Table and some methods for the prediction of the properties of the super-heavy elements. The Periodic Table is next explored in various dimensions other than two. The natural clustering of the elements into groups is studied by three different but complementary routes, namely via the topological structures of the groups, the self-association of the elements as evidenced by neural network studies, and information theoretical analysis of the behaviour of atoms. Following a detailed investigation of the mathematical basis for the periodicity seen in atomic and molecular spectroscopy, three separate presentations delve into many different aspects of the group-theoretical structure of the Periodic Table. The unusual combination of themes offered here will appeal to all who seek a more detailed and intimate knowledge of the Periodic Table than that available in standard texts on the subject.