Coherent states and applications in mathematical physics. (English) Zbl 1243.81004

Combescure, Monique; Robert, Didier

Theoretical and Mathematical Physics (Cham). Berlin: Springer (ISBN 978-94-007-0195-3/hbk; 978-94-007-0196-0/ebook). xiii, 415 p. (2012).

The coherent state has played a very important role in theoretical physics and mathematical physics during almost a century. The field of applications of coherent states is very wide. The research of coherent state is one of the hot research fields of theoretical physicists and mathematical physicists in the world today. In this book, the authors elaborate the canonical Gaussian Coherent States and their applications. The authors also describe extensions of coherent states systems to other geometric settings. Finally, in the appendices the authors explain how this is used to build generalized coherent systems in the sense of Gilmore-Perelomov.
This book is a masterpiece at present. The material covered in this book is designed for an advanced graduate student or researcher. The one-parameter coherent states today have caused a great interest for scholars. The authors introduce well into this topic.

Reviewer: Chen Yong-Qing (Shenzhen)

MSC:

81R30	Coherent states
81-02	Research exposition (monographs, survey articles) pertaining to quantum theory
81P40	Quantum coherence, entanglement, quantum correlations

Keywords:

coherent states; supercoherent states; Lie superalgebra