Coherent states and their generalizations - A mathematical overview
(1995) Reviews in Mathematical Physics : a journal for survey and expository articles in the field of mathematical physics — Vol. 7, n° 7, p. 1013-1104 (1995)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- We present a survey of the theory of coherent states (CS); and some of their generalizations, with emphasis on the mathematical structure, rather than on physical applications. Starting from the standard theory of CS over Lie groups, we develop a general formalism, in which CS are associated to group representations which are square integrable over a homogeneous space. A further step allows us to dispense with the group context altogether, and thus obtain the so-called reproducing triples and continuous frames introduced in some earlier work. We discuss in detail a number of concrete examples, namely semisimple Lie groups, the relativity groups and various types of wavelets. Finally we turn to some physical applications, centering on quantum measurement and the quantization/dequantization problem, that is, the transition from the classical to the quantum level and vice versa.
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Citations
Ali, ST., Antoine, J.-P., Gazeau, JP., & Mueller, UA. (1995). Coherent states and their generalizations - A mathematical overview. Reviews in Mathematical Physics : a journal for survey and expository articles in the field of mathematical physics, 7(7), 1013-1104. https://doi.org/10.1142/S0129055X95000396 (Original work published 1995)