N MUKUNDA*

Centre for Theoretical Studies and Department of Physics, Indian Institute of Science,  Bangalore 560 012, India

* Honorary Professor, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur,  Bangalore 560 064, India

Abstract.

The main properties of standard quantum mechanical coherent states and the two generalizations of Klauder and of Perelomov are reviewed. For a system of generalized coherent states in the latter sense, necessary and sufficient conditions for existence of a diagonal coherent stable representation for all Hilbert-Schmidt operators are obtained. The main ingredients are Clebsch-Gordan theory and induced representation theory.

Keywords: Generalized coherent states; diagonal representation; induced representation theory.

Pacs Nos. 03.65.-w; 03.65.Ca; 02.20.Qs