Abstract:
Completeness is proved for some subsystems of a system of coherent states. The liaear
dependence of states is investigated for von Neumann type subsystems. A detailed study is
made of the case when a regular lattice on the complex $\alpha$ plane with cell area $S=\pi$ corresponds
to the states of the system. It is shown that in this case there exists only one linear
relationship between the coherent states. This relationship is equivalent to an infinite set
of identities, of which the simplest can also be obtained by means of the transformation
formulas for $\theta$ functions.
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