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# 📙 Group Representation for Quantum Theory by Masahito Hayashi (auth.) — 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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Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the a...

Illustrating the fascinating interplay between physics and mathematics, Groups, Representations and Physics, Second Edition provides a solid foundation in the theory of groups, particularly group representations. For this new, fully revised edition, the a...

This volume contains invited articles by top-notch experts who focus on such topics as: modular representations of algebraic groups, representations of quantum groups and crystal bases, representations of affine Lie algebras, representations of affine Hec...

This book introduces systematically the eigenfunction method, a new approach to the group representation theory which was developed by the authors in the 1970's and 1980's in accordance with the concept and method used in quantum mechanics. It covers the ...

Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac, and whose definitive mathematical formulation is due to von Neuma...

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...

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathemati...

Книга Group Representations: Background Material Group Representations: Background MaterialКниги English литература Автор: Gregory Karpilovsky Год издания: 1992 Формат: pdf Издат.:Elsevier Science Страниц: 669 Размер: 21,7 ISBN: 044488632X Язык: Английски...

This Third Edition, like its two predecessors, provides a detailed account of the basic theory needed to understand the properties of light and its interactions with atoms, in particular the many nonclassical effects that have now been observed in quantum...

Database systems and database design technology have undergone significant evolution in recent years. The relational data model and relational database systems dominate business applications; in turn, they are extended by other technologies like data w...

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Tarot Plain and Simple by Anthony Louis is the book you've been waiting for! As the title indicates, this book presents the Tarot in clear language that anyone can understand. If you've had trouble learning the Tarot, this book gives the meaning of each a...

For 250 years a large tract of oak savannah at the mouth of the Niagara River designated as a Military Reserve has witnessed a rich military and political history: the site of the first parliament of Upper Canada; a battleground during the War of 1812; a...

The book "TransMath - Innovative Solutions from Mathematical Technology" has been conceived as a tool for the dissemination of scientific knowledge. This publication is addressed to those companies with innovation needs that could be met through mathemat...

While there are several texts on how to solve and analyze stochastic programs, this is the first text to address basic questions about how to model uncertainty, and how to reformulate a deterministic model so that it can be analyzed in a stochastic setti...

An engaging look at the road to a sustained economic recoveryThe global finance system can be regulated to prevent massive credit fraud, tame capitalism, confront the sovereign debt crisis, and move towards investing in the real economy and full employmen...