Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 1

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Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 1

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Author : Vladimir Dobrev
language : en
Publisher: Springer
Release Date : 2018-11-28

Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 1 written by Vladimir Dobrev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-28 with Mathematics categories.

This book is the first volume of proceedings from the joint conference X International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), held on 19–25 June 2017 in Varna, Bulgaria. The QTS series was founded on the core principle that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium at the forefront of theoretical and mathematical physics. The LT series covers the whole field of Lie theory in its widest sense, together with its applications in many areas of physics. As an interface between mathematics and physics, the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In dividing the material between the two volumes, the Editor has sought to select papers that are more oriented toward mathematics for the first volume, and those focusing more on physics for the second. However, this division is relative, since many papers are equally suitable for either volume. The topics addressed in this volume represent the latest trends in the fields covered by the joint conferences: representation theory, integrability, entanglement, quantum groups, number theory, conformal geometry, quantum affine superalgebras, noncommutative geometry. Further, they present various mathematical results: on minuscule modules, symmetry breaking operators, Kashiwara crystals, meta-conformal invariance, the superintegrable Zernike system.

Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 2

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Author : Vladimir Dobrev
language : en
Publisher: Springer
Release Date : 2018-09-30

Quantum Theory And Symmetries With Lie Theory And Its Applications In Physics Volume 2 written by Vladimir Dobrev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-30 with Science categories.

This book is the second volume of the proceedings of the joint conference X. International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII. International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), 19–25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers of theoretical and mathematical physics. The LT series covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mathematicians and theoretical and mathematical physicists. In the division of the material between the two volumes, the Editor has tried to select for the first and second volumes papers that are more oriented toward mathematics and physics, respectively. However, this division is relative since many papers could have been placed in either volume. The topics covered in this volume represent the most modern trends in the fields of the joint conferences: symmetries in string theories, conformal field theory, holography, gravity theories and cosmology, gauge theories, foundations of quantum theory, nonrelativistic and classical theories.

Lie Theory And Its Applications In Physics

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Author : Vladimir Dobrev
language : en
Publisher: Springer Nature
Release Date : 2020-10-15

Lie Theory And Its Applications In Physics written by Vladimir Dobrev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-15 with Science categories.

This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Symmetry In Geometry And Analysis Volume 1

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Author : Michael Pevzner
language : en
Publisher: Springer Nature
Release Date : 2025-02-09

Symmetry In Geometry And Analysis Volume 1 written by Michael Pevzner and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-09 with Mathematics categories.

Symmetry in Geometry and Analysis is a Festschrift honoring Toshiyuki Kobayashi. The three volumes feature 35 selected contributions from invited speakers of twin conferences held in June 2022 in Reims, France, and in September 2022 in Tokyo, Japan. These contributions highlight the profound impact of Prof. Kobayashi’s pioneering ideas, groundbreaking discoveries, and significant achievements in the development of analytic representation theory, noncommutative harmonic analysis, and the geometry of discontinuous groups beyond the Riemannian context, among other areas, over the past four decades. The first volume of the Festschrift includes a survey article on Kobayashi’s innovative contributions to Mathematics, emphasizing their influence and introducing new perspectives across various fields. Original articles contained in Volume 1 focus on differential geometry with symmetries as well as algebraic and geometric aspects of representation theory of reductive Lie groups and related topics. Contributions are by Velleda Baldoni, Dan Barbasch, Leticia Barchini, Sigiswald Barbier, Yves Benoist, Sam Claerebout, Michael Eastwood, Wee Teck Gan, William M. Goldman, Roger Howe, Kazuki Kannaka, Toshihisa Kubo, Hung Yean Loke, Jia-Jun Ma, Reiko Miyaoka, Kento Ogawa, Takayuki Okuda, Yoshiki Oshima, Paul-Émile Paradan, Annegret Paul, Michael Pevzner, Yiannis Sakellaridis, Atsumi Sasaki, Gordan Savin, Hideko Sekiguchi, Binyong Sun, Yuichiro Tanaka, Koichi Tojo, Peter Trapa, Michèle Vergne, Joseph A. Wolf, Kayue Daniel Wong, and Chen-Bo Zhu. The Mathematical Work of Toshiyuki Kobayashi is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

An Introduction To Covariant Quantum Mechanics

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Author : Josef Janyška
language : en
Publisher: Springer Nature
Release Date : 2022-04-06

An Introduction To Covariant Quantum Mechanics written by Josef Janyška and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-06 with Science categories.

This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.

Lie And Non Lie Symmetries Theory And Applications For Solving Nonlinear Models

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Author : Roman M. Cherniha
language : en
Publisher: MDPI
Release Date : 2018-07-06

Lie And Non Lie Symmetries Theory And Applications For Solving Nonlinear Models written by Roman M. Cherniha and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-06 with Mathematics categories.

This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry

Spectral Theory And Quantum Mechanics

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Author : Valter Moretti
language : en
Publisher: Springer
Release Date : 2018-01-30

Spectral Theory And Quantum Mechanics written by Valter Moretti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.

This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."

Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications

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Author : Alexey P Isaev
language : en
Publisher: World Scientific
Release Date : 2020-07-16

Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications written by Alexey P Isaev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-16 with Science categories.

This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

Interactions Of Quantum Affine Algebras With Cluster Algebras Current Algebras And Categorification

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Author : Jacob Greenstein
language : en
Publisher: Springer Nature
Release Date : 2022-03-11

Interactions Of Quantum Affine Algebras With Cluster Algebras Current Algebras And Categorification written by Jacob Greenstein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-11 with Mathematics categories.

This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.

Integrability Supersymmetry And Coherent States

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Author : Şengül Kuru
language : en
Publisher: Springer
Release Date : 2019-07-12

Integrability Supersymmetry And Coherent States written by Şengül Kuru and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-12 with Science categories.

This volume shares and makes accessible new research lines and recent results in several branches of theoretical and mathematical physics, among them Quantum Optics, Coherent States, Integrable Systems, SUSY Quantum Mechanics, and Mathematical Methods in Physics. In addition to a selection of the contributions presented at the "6th International Workshop on New Challenges in Quantum Mechanics: Integrability and Supersymmetry", held in Valladolid, Spain, 27-30 June 2017, several high quality contributions from other authors are also included. The conference gathered 60 participants from many countries working in different fields of Theoretical Physics, and was dedicated to Prof. Véronique Hussin—an internationally recognized expert in many branches of Mathematical Physics who has been making remarkable contributions to this field since the 1980s. The reader will find interesting reviews on the main topics from internationally recognized experts in each field, as well as other original contributions, all of which deal with recent applications or discoveries in the aforementioned areas.