Vector coherent state representations, induced representations and geometric quantization: II. Vector coherent state representations
نویسندگان
چکیده
منابع مشابه
Vector coherent state representations, induced representations, and geometric quantization: II. Vector coherent state representations
It is shown here and in the preceeding paper [1] that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of genera...
متن کاملua nt - p h / 02 01 13 0 v 1 2 8 Ja n 20 02 Vector coherent state representations , induced representations , and geometric quantization : II . Vector coherent state representations
It is shown here and in the preceeding paper [1] that vector coherent state theory, the theory of induced representations, and geometric quantization provide alternative but equivalent quantizations of an algebraic model. The relationships are useful because some constructions are simpler and more natural from one perspective than another. More importantly, each approach suggests ways of genera...
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Coherent state theory is shown to reproduce three categories of representations of the spectrum generating algebra for an algebraic model: (i) classical realizations which are the starting point for geometric quantization; (ii) induced unitary representations corresponding to prequantization; and (iii) irreducible unitary representations obtained in geometric quantization by choice of a polariz...
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It is shown that, for both compact and non-compact Lie groups, vector-coherent-state methods provide straightforward derivations of holomorphic representations on symmetric spaces. Complementary vector-coherent-state methods are introduced to derive pairs of holomorphic representations which are bi-orthogonal duals of each other with respect to a simple Bargmann inner product. It is then shown ...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2002
ISSN: 0305-4470
DOI: 10.1088/0305-4470/35/27/307