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Coherent states and induced representations

✍ Scribed by H. Scutaru

Publisher
Springer
Year
1977
Tongue
English
Weight
344 KB
Volume
2
Category
Article
ISSN
0377-9017

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✦ Synopsis

A generalization of the notion of coherent states is given. The following one-to-one correspondences are pointed out: (1)between covariant overcomplete systems of coherent states and a class of covariant semi-spectral measures; (2)between covariant semispectral measures and unitary irreducible subrepresentations of induced representations of Lie groups; (3)between unitary irreducible representations of Lie groups with covariant overcomplete systems of coherent states and unitary irreducible subrepresentations of induced representations, whose representation spaces are reproducing kernel Hilbert spaces.

πŸ“œ SIMILAR VOLUMES

On the coherent state representation of
On the coherent state representation of linear operators
✍ M. Romerio πŸ“‚ Article πŸ“… 1977 πŸ› Springer 🌐 English βš– 199 KB

It is shown that the possibility of representing every operator, acting on a vector space, irreducible under SU(2), in the form f 1~2 ) G(~2) (~21 d~2 [1], where {t~2)) is a set of Bloch (atomic) coherent states, can be generalized to compact semi-simple Lie groups. In a now classic paper [1 ], the