m at h . D G ] 1 4 Ju l 1 99 8 COHERENT STATES AND GEOMETRY
نویسنده
چکیده
The coherent states are viewed as a powerful tool in differential geometry. It is shown that some objects in differential geometry can be expressed using quantities which appear in the construction of the coherent states. The following subjects are discussed via the coherent states: the geodesics, the conjugate locus and the cut locus; the divisors; the Calabi's diastasis and its domain of definition; the Euler-Poincaré characteristic of the manifold, the number of Borel-Morse cells, Kodaira embeding theorem....
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ar X iv : d g - ga / 9 70 70 26 v 1 3 1 Ju l 1 99 7 COHERENT STATES , TRANSITION AMPLITUDES AND EMBEDDINGS
The transition amplitudes between coherent states on the coherent state manifold M are expressed in terms of the embedding of M into a projective Hilbert space PL. Consequences for the dimension of PL and a simple geometric interpretation of Calabi's diastasis follows. The coherent states [1] offer a powerful framework to formulate a link between classical and quantum mechanics [2, 3]. Simultan...
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It is shown how the coherent states permit to find different geometrical objects as the geodesics, the conjugate locus, the cut locus, the Calabi’s diastasis and its domain of definition, the Euler-Poincaré characteristic, the number of Borel-Morse cells, the Kodaira embedding theorem. 1 Coherent state manifold and coherent vector manifold In this talk the coherent states [] are presented as a ...
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تاریخ انتشار 1998