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# ðŸ“™ Group Representation for Quantum Theory by Masahito Hayashi (auth.) â€” download pdf

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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.

- Author:
**Masahito Hayashi (auth.)** - Year:
**2017** - Publisher:
**Springer International Publishing** - Language:
**English** - ISBN:
**978-3-319-44906-7,978-3-319-44904-3**

- File size:
**5 713 113** - Format:
**pdf**

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While applications rapidly change one to the next in our commercialized world, fundamental principles behind those applications remain constant. So if one understands those principles well enough and has ample experience in applying them, he or sh...

This volume contains the proceedings of the conference on Spectral and Scattering Theory for Quantum Magnetic Systems, which took place at CIRM, Luminy, France, in July 2008. The main purpose of this conference was to bring together a number of specialist...

Designed as an introduction to harmonic analysis and group representations, this book covers a wide range of topics rather than delving deeply into any particular one. In the words of H. Weyl "...it is primarily meant for the humble, who want to learn as ...

The theory and applications of C*-algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C*-algebras is also reg...

The ultimate modern textbook on Quantum Theory, this graduate-level and self-contained s text is also a reference and research work which provides background for researchers in this discipline, covering important recent developments and most aspects of th...

The author has put serious work and thought to writing this excellent book. It is a graduate level exploration of quantum theory but it is written very clearly. A background in college level physics and mathematics are necessary of course but the book is ...

Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This third volume of The Quantum Theory of Fields presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of the...

This book is a critical introduction to the long-standing debate concerning the conceptual foundations of quantum mechanics and the problems it has posed for physicists and philosophers from Einstein to the present. Quantum theory has been a major infulen...

This book constitutes the thoroughly refereed post-workshop proceedings of the First International Workshop on Knowledge Representation for Agents and Multi-Agent Systems, KRAMAS 2008, held in Sydney, Australia, in September 2008 as a satellite event of K...