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The coherent states: old geometrical methods in new quantum clothes

Stefan Berceanu
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Abstract

A geometric characterization of transition amplitudes between coherent states, or equivalently, of the hermitian scalar product of holomorphic cross sections in the associated D - M tilda - module, in terms of the embedding of the cohe- rent state manifold M-tilda into a projective Hilbert space is proposed. Cohe- rent state manifolds endowed with a homogeneous kaehler structure are conside- red. Using the coherent state approach, an effective method to find the cut loci on symmetric manifolds and generalized symmetric manifolds M-tilda is proposed. The CW - complex structure of coherent state manifolds of flag type is discussed. Recent results of Anandan and Aharonov are commented vis-a-vis of last century constructions in projective geometry. Calculations with signi- ficance in coherent state approch furnish explicit proofs of the results announ- ced by Y. C. Wong on conjugate locus in complex Grassmann manifold.

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Stefan Berceanu. 1994-08-02. The coherent states: old geometrical methods in new quantum clothes. https://arxiv.org/abs/hep-th/9408008

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