The Resource Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource)

Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource)

Label
Group Representation for Quantum Theory
Title
Group Representation for Quantum Theory
Statement of responsibility
by Masahito Hayashi
Creator
Contributor
Author
Provider
Subject
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, 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
http://library.link/vocab/creatorName
Hayashi, Masahito
Image bit depth
0
LC call number
QC173.96-174.52
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)
Instantiates
Publication
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
10.1007/978-3-319-44906-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-44906-7
Label
Group Representation for Quantum Theory, by Masahito Hayashi, (electronic resource)
Publication
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
10.1007/978-3-319-44906-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-319-44906-7

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