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1 Hayashi, Masahito A Group Theoretic Approach to Quantum Information I10174 2017 eBook  
2 Hayashi, Masahito Group Representation for Quantum Theory I10118 2017 eBook  
3 Cicogna, Giampaolo Exercises and Problems in Mathematical Methods of Physics I09803 2018 eBook  
4 Konno, Hitoshi Elliptic Quantum Groups I09584 2020 eBook  
5 Kota, V. K. B SU(3) Symmetry in Atomic Nuclei I08915 2020 eBook  
6 Cicogna, Giampaolo Exercises and Problems in Mathematical Methods of Physics I08828 2020 eBook  
7 Coecke, Bob Current Research in Operational Quantum Logic I11348 2000 eBook  
8 Cassinelli, Gianni The Theory of Symmetry Actions in Quantum Mechanics I11185 2004 eBook  
9 Kramer, Peter Coverings of Discrete Quasiperiodic Sets I11119 2003 eBook  
10 Liboff, Richard Primer for Point and Space Groups I10645 2004 eBook  
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TitleA Group Theoretic Approach to Quantum Information
Author(s)Hayashi, Masahito
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXIII, 228 p. 32 illus : online resource
Abstract NoteThis textbook is the first one addressing quantum information from the viewpoint of group symmetry. Quantum systems have a group symmetrical structure. This structure enables to handle systematically quantum information processing. However, there is no other textbook focusing on group symmetry for quantum information although there exist many textbooks for group representation. After the mathematical preparation of quantum information, this book discusses quantum entanglement and its quantification by using group symmetry. Group symmetry drastically simplifies the calculation of several entanglement measures although their calculations are usually very difficult to handle. This book treats optimal information processes including quantum state estimation, quantum state cloning, estimation of group action and quantum channel etc. Usually it is very difficult to derive the optimal quantum information processes without asymptotic setting of these topics. However, group symmetry allows to derive these optimal solutions without assuming the asymptotic setting. Next, this book addresses the quantum error correcting code with the symmetric structure of Weyl-Heisenberg groups. This structure leads to understand the quantum error correcting code systematically. Finally, this book focuses on the quantum universal information protocols by using the group SU(d). This topic can be regarded as a quantum version of the Csiszar-Korner's universal coding theory with the type method. The required mathematical knowledge about group representation is summarized in the companion book, Group Representation for Quantum Theory
ISBN,Price9783319452418
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GROUP THEORY 4. Group Theory and Generalizations 5. QUANTUM COMPUTERS 6. Quantum computing 7. Quantum Information Technology, Spintronics 8. QUANTUM PHYSICS 9. Security Science and Technology 10. SPINTRONICS 11. System safety
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TitleGroup Representation for Quantum Theory
Author(s)Hayashi, Masahito
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXXVIII, 338 p. 54 illus., 1 illus. in color : online resource
Abstract NoteThis book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SU(d), Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including projective representation. Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematical style and, often, the materials are too segmented. At least, the notation is not familiar to people working with quantum theory. Others are good elementary books, but do not deal with topics related to quantum theory. In particular, such elementary books do not cover projective representation, which is more important in quantum theory. On the other hand, there are several books for physicists. However, these books are too simple and lack the detailed discussion. Hence, they are not useful for advanced study even in physics. To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g. Next, this book discusses Lie group and Lie algebra. This part starts with the basics knowledge, and proceeds to the special groups, e.g., SU(2), SU(1,1), and SU(d). After the special groups, it explains concrete applications to physical systems, e.g., angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, and quark model. Then, it proceeds to the general theory for Lie group and Lie algebra. Using this knowledge, this book explains the Bosonic system, which has the symmetries of Heisenberg group and the squeezing symmetry by SL(2,R) and Sp(2n,R). Finally, as the discrete version, this book treats the discrete Heisenberg representation which is related to quantum error correction. To enhance readers' undersnding, this book contains 54 figures, 23 tables, and 111 exercises with solutions
ISBN,Price9783319449067
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GROUP THEORY 4. Group Theory and Generalizations 5. MATHEMATICAL PHYSICS 6. QUANTUM COMPUTERS 7. Quantum computing 8. Quantum Information Technology, Spintronics 9. QUANTUM PHYSICS 10. SPINTRONICS
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TitleExercises and Problems in Mathematical Methods of Physics
Author(s)Cicogna, Giampaolo
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2018.
DescriptionX, 182 p. 8 illus : online resource
Abstract NoteThis book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students of mathematics, chemistry, and engineering, as well as their teachers, will also find it of value.
ISBN,Price9783319761657
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. FOURIER ANALYSIS 4. Functions of a Complex Variable 5. FUNCTIONS OF COMPLEX VARIABLES 6. GROUP THEORY 7. Group Theory and Generalizations 8. INTEGRAL TRANSFORMS 9. Integral Transforms, Operational Calculus 10. Mathematical Methods in Physics 11. Operational calculus 12. OPERATOR THEORY 13. PHYSICS
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TitleElliptic Quantum Groups : Representations and Related Geometry
Author(s)Konno, Hitoshi
PublicationSingapore, 1. Imprint: Springer 2. Springer Singapore, 2020.
DescriptionXIII, 131 p. 3 illus : online resource
Abstract NoteThis is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization, explicit construction of both finite and infinite-dimensional representations, and a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups. In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions. The author???s recent study showed that these elliptic weight functions are identified with Okounkov???s elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov???s geometric approach to quantum integrable systems is a rapidly growing topic in mathematical physics related to the Bethe ansatz, the Alday-Gaiotto-Tachikawa correspondence between 4D SUSY gauge theories and the CFT???s, and the Nekrasov-Shatashvili correspondences between quantum integrable systems and quantum cohomology. To invite the reader to such topics is one of the aims of this book
ISBN,Price9789811573873
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. GROUP THEORY 5. Group Theory and Generalizations 6. Mathematical Applications in the Physical Sciences 7. MATHEMATICAL PHYSICS 8. Order, Lattices, Ordered Algebraic Structures 9. Ordered algebraic structures
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TitleSU(3) Symmetry in Atomic Nuclei
Author(s)Kota, V. K. B
PublicationSingapore, 1. Imprint: Springer 2. Springer Singapore, 2020.
DescriptionXV, 289 p. 37 illus., 4 illus. in color : online resource
Abstract NoteThis book provides an understandable review of SU(3) representations, SU(3) Wigner???Racah algebra and the SU(3) ??? SO(3) integrity basis operators, which are often considered to be difficult and are avoided by most nuclear physicists. Explaining group algebras that apply to specific physical systems and discussing their physical applications, the book is a useful resource for researchers in nuclear physics. At the same time it helps experimentalists to interpret data on rotational nuclei by using SU(3) symmetry that appears in a variety of nuclear models, such as the shell model, pseudo-SU(3) model, proxy-SU(3) model, symplectic Sp(6, R) model, various interacting boson models, various interacting boson???fermion models, and cluster models. In addition to presenting the results from all these models, the book also describes a variety of statistical results that follow from the SU(3) symmetry
ISBN,Price9789811536038
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GROUP THEORY 4. Group Theory and Generalizations 5. MATHEMATICAL PHYSICS 6. NUCLEAR PHYSICS 7. Particle and Nuclear Physics 8. SOLID STATE PHYSICS
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TitleExercises and Problems in Mathematical Methods of Physics
Author(s)Cicogna, Giampaolo
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2020.
DescriptionXII, 218 p. 9 illus : online resource
Abstract NoteThis book is the second edition, whose original mission was to offer a new approach for students wishing to better understand the mathematical tenets that underlie the study of physics. This mission is retained in this book. The structure of the book is one that keeps pedagogical principles in mind at every level. Not only are the chapters sequenced in such a way as to guide the reader down a clear path that stretches throughout the book, but all individual sections and subsections are also laid out so that the material they address becomes progressively more complex along with the reader's ability to comprehend it. This book not only improves upon the first in many details, but it also fills in some gaps that were left open by this and other books on similar topics. The 350 problems presented here are accompanied by answers which now include a greater amount of detail and additional guidance for arriving at the solutions. In this way, the mathematical underpinnings of the relevant physics topics are made as easy to absorb as possible.
ISBN,Price9783030594725
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. FOURIER ANALYSIS 4. Functions of a Complex Variable 5. FUNCTIONS OF COMPLEX VARIABLES 6. GROUP THEORY 7. Group Theory and Generalizations 8. INTEGRAL TRANSFORMS 9. Integral Transforms, Operational Calculus 10. Mathematical Methods in Physics 11. Operational calculus 12. OPERATOR THEORY 13. PHYSICS
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TitleCurrent Research in Operational Quantum Logic : Algebras, Categories, Languages
Author(s)Coecke, Bob;Moore, David;Wilce, Alexander
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2000.
DescriptionVII, 325 p : online resource
Abstract NoteThe present volume has its origins in a pair of informal workshops held at the Free University of Brussels, in June of 1998 and May of 1999, named "Current Research 1 in Operational Quantum Logic". These brought together mathematicians and physicists working in operational quantum logic and related areas, as well as a number of interested philosophers of science, for a rare opportunity to discuss recent developments in this field. After some discussion, it was decided that, rather than producing a volume of conference proceedings, we would try to organize the conferees to produce a set of comprehensive survey papers, which would not only report on recent developments in quantum logic, but also provide a tutorial overview of the subject suitable for an interested non-specialist audience. The resulting volume provides an overview of the concepts and methods used in current research in quantum logic, viewed both as a branch of mathemati?? cal physics and as an area of pure mathematics. The first half of the book is concerned with the algebraic side of the subject, and in particular the theory of orthomodular lattices and posets, effect algebras, etc. In the second half of the book, special attention is given to categorical methods and to connections with theoretical computer science. At the 1999 workshop, we were fortunate to hear three excellent lectures by David J. Foulis, represented here by two contributions. Dave's work, spanning 40 years, has helped to define, and continues to reshape, the field of quantum logic
ISBN,Price9789401712019
Keyword(s)1. ALGEBRA 2. Applications of Mathematics 3. APPLIED MATHEMATICS 4. Category theory (Mathematics) 5. Category Theory, Homological Algebra 6. EBOOK 7. EBOOK - SPRINGER 8. ENGINEERING MATHEMATICS 9. GROUP THEORY 10. Group Theory and Generalizations 11. Homological algebra 12. Order, Lattices, Ordered Algebraic Structures 13. Ordered algebraic structures 14. QUANTUM PHYSICS
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TitleThe Theory of Symmetry Actions in Quantum Mechanics : with an Application to the Galilei Group
Author(s)Cassinelli, Gianni;Vito, Ernesto;Levrero, Alberto;Lahti, Pekka J
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2004.
DescriptionXII, 111 p : online resource
Abstract NoteThis is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given
ISBN,Price9783540445098
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GROUP THEORY 4. Group Theory and Generalizations 5. LIE GROUPS 6. Mathematical Methods in Physics 7. PHYSICS 8. QUANTUM PHYSICS 9. TOPOLOGICAL GROUPS 10. Topological Groups, Lie Groups
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TitleCoverings of Discrete Quasiperiodic Sets : Theory and Applications to Quasicrystals
Author(s)Kramer, Peter;Papadopolos, Zorka
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2003.
DescriptionXV, 273 p : online resource
Abstract NoteCoverings are efficient ways to exhaust Euclidean N-space with congruent geometric objects. Discrete quasiperiodic systems are exemplified by the atomic structure of quasicrystals. The subject of coverings of discrete quasiperiodic sets emerged in 1995. The theory of these coverings provides a new and fascinating perspective of order down to the atomic level. The authors develop concepts related to quasiperiodic coverings and describe results. Specific systems in 2 and 3 dimensions are described with many illustrations. The atomic positions in quasicrystals are analyzed
ISBN,Price9783540458050
Keyword(s)1. CRYSTALLOGRAPHY 2. Crystallography and Scattering Methods 3. EBOOK 4. EBOOK - SPRINGER 5. GROUP THEORY 6. Group Theory and Generalizations 7. Phase transitions (Statistical physics) 8. Phase Transitions and Multiphase Systems
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TitlePrimer for Point and Space Groups
Author(s)Liboff, Richard
PublicationNew York, NY, 1. Imprint: Springer 2. Springer New York, 2004.
DescriptionXIV, 220 p : online resource
Abstract NoteThis text stems from a course I have taught a number of times, attended by students of material science, electrical engineering, physics, chemistry, physical chemistry and applied mathematics. It is intended as an intro?? ductory discourse to give the reader a first encounter with group theory. The work concentrates on point and space groups as these groups have the principal application in technology. Here is an outline of the salient features of the chapters. In Chapter 1, basic notions and definitions are introduced including that of Abelian groups, cyclic groups, Sylow's theorems, Lagrange's subgroup theorem and the rearrangement theorem. In Chapter 2, the concepts of classes and direct products are discussed. Applications of point groups to the Platonic solids and non-regular dual polyhedra are described. In Chapter 3, matrix representation of operators are introduced leading to the notion of irreducible representations ('irreps'). The Great Orthogonal?? ity Theorem (GOT) is also introduced, followed by six important rules relating to dimensions of irreps. Schur's lemma and character tables are described. Applications to quantum mechanics are discussed in Chapter 4 including descriptions of the rotation groups in two and three dimensions, the symmetric group, Cayley's theorem and Young diagrams. The relation of degeneracy of a quantum state of a system to dimensions of irreps of the group of symmetries of the system are discussed, as well as the basis properties of related eigenfunctions
ISBN,Price9781468493832
Keyword(s)1. CONDENSED MATTER 2. CONDENSED MATTER PHYSICS 3. EBOOK 4. EBOOK - SPRINGER 5. ELECTRICAL ENGINEERING 6. GROUP THEORY 7. Group Theory and Generalizations 8. PHYSICAL CHEMISTRY 9. PHYSICS 10. Physics, general
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