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The Resource Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource)
Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource)
Resource Information
The item Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This 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, hydrogentype Hamiltonian, spinorbit 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, hydrogentype Hamiltonian, spinorbit 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
 Language
 eng
 Extent
 XXVIII, 338 p. 54 illus., 1 illus. in color.
 Contents

 Foundation of Quantum Theory
 Group Representation
 Representations of Lie Group and Lie Algebra (Basics)
 Representations of Lie Group and Lie Algebra (Special Case)
 Representations of Lie Group and Lie Algebra (General Case)
 Bosonic System
 Discretization of Bosonic System
 Isbn
 9783319449067
 Label
 Group Representation for Quantum Theory
 Title
 Group Representation for Quantum Theory
 Statement of responsibility
 by Masahito Hayashi
 Subject

 Mathematical physics
 Mathematical physics
 Physics
 Physics
 Physics
 Quantum Computing
 Quantum Information Technology, Spintronics
 Quantum Physics
 Electronic resources
 Quantum computers
 Quantum computers
 Quantum physics
 Quantum physics
 Spintronics
 Spintronics
 Quantum Physics
 Group Theory and Generalizations
 Group theory
 Group theory
 Mathematical Physics
 Mathematical Physics
 Language
 eng
 Summary
 This 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, hydrogentype Hamiltonian, spinorbit 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, hydrogentype Hamiltonian, spinorbit 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
 http://library.link/vocab/creatorName
 Hayashi, Masahito
 Image bit depth
 0
 LC call number
 QC173.96174.52
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 SpringerLink
 http://library.link/vocab/subjectName

 Physics
 Group theory
 Quantum computers
 Mathematical physics
 Quantum physics
 Spintronics
 Physics
 Quantum Physics
 Group Theory and Generalizations
 Quantum Information Technology, Spintronics
 Quantum Computing
 Mathematical Physics
 Label
 Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Foundation of Quantum Theory  Group Representation  Representations of Lie Group and Lie Algebra (Basics)  Representations of Lie Group and Lie Algebra (Special Case)  Representations of Lie Group and Lie Algebra (General Case)  Bosonic System  Discretization of Bosonic System
 Dimensions
 unknown
 Extent
 XXVIII, 338 p. 54 illus., 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319449067
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319449067
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319449067
 Label
 Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 Foundation of Quantum Theory  Group Representation  Representations of Lie Group and Lie Algebra (Basics)  Representations of Lie Group and Lie Algebra (Special Case)  Representations of Lie Group and Lie Algebra (General Case)  Bosonic System  Discretization of Bosonic System
 Dimensions
 unknown
 Extent
 XXVIII, 338 p. 54 illus., 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319449067
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319449067
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319449067
Subject
 Mathematical physics
 Mathematical physics
 Physics
 Physics
 Physics
 Quantum Computing
 Quantum Information Technology, Spintronics
 Quantum Physics
 Electronic resources
 Quantum computers
 Quantum computers
 Quantum physics
 Quantum physics
 Spintronics
 Spintronics
 Quantum Physics
 Group Theory and Generalizations
 Group theory
 Group theory
 Mathematical Physics
 Mathematical Physics
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