Group Representation for Quantum Theory

Masahito Hayashi was born in Japan in 1971. He received the B.S. degree from the Faculty of Sciences in Kyoto University, Japan, in 1994 and the M.S. and Ph.D. degrees in Mathematics from Kyoto University, Japan, in 1996 and 1999, respectively. He worked in Kyoto University as a Research Fellow of the Japan Society of the Promotion of Science (JSPS) from 1998 to 2000, and worked in the Laboratory for Mathematical Neuroscience, Brain Science Institute, RIKEN from 2000 to 2003, and worked in ERATO Quantum Computation and Information Project, Japan Science and Technology Agency (JST) as the Research Head from 2000 to 2006. He also worked in the Superrobust Computation Project Information Science and Technology Strategic Core (21st Century COE by MEXT) Graduate School of Information Science and Technology, The University of Tokyo as Adjunct Associate Professor from 2004 to 2007. He worked in the Graduate School of Information Sciences, Tohoku University as Associate Professor from 2007 to 2012. In 2012, he joined the Graduate School of Mathematics, Nagoya University as Professor. He also worked in Centre for Quantum Technologies, National University of Singapore as Visiting Research Associate Professor from 2009 to 2012 and as Visiting Research Professor from 2012 to now. In 2011, he received the Information Theory Society Paper Award (2011) for Information-Spectrum Approach to Second-Order Coding Rate in Channel Coding. In 2016, he received the Japan Academy Medal from the Japan Academy and the JSPS Prize from Japan Society for the Promotion of Science.

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.

"The book is well organized. Crucial notions such as highest weight representations or coherent states are introduced, first in special cases and then generalized step by step. ... There is also a quite useful index of notation in the form of 8 tablets, each table grouping symbols of a given type. The presentation of representation theory of compact groups and the Heisenberg group is quite good." (Wojciech Lisiecki, Mathematical Reviews, March, 2018)

"This book not only fills a pedagogical gap in the literature, it moreover presents a current view of the problems being considered in research. ... Nonexperts should be able to learn much about the various fields this books treats, and the specialist profit from the unusual approach that enlightens some formal aspects. The reviewer firmly believes that this textbook will become a canonical reference for students of quantum physics in the coming years." (Rutwig Campoamor-Stursberg, zbMATH 1367.81004, 2017)