Coherent states of SU(N) groups

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Abstract
An explicit and uniform construction for coherent states (CS) for all the SU(N) groups is given and, on this basis, their properties are investigated. The CS are parametrized by the dots of a coset space, which is, in this particular case, the projective space CPN-1 and which plays the role of the phase space in the corresponding classical mechanics. The logarithm of the modulus of the CS overlap, being interpreted as assymmetric in the space, gives the Fubini-Study metric in CPN-1. The classical limit is investigated in terms of operator symbols. h=P-1 (where P is the signature of the representation) plays the role of Planck's constant. The classical limit of the so called star commutator of the symbols generates the Poisson bracket in the corresponding phase space. The CS form an overcompleted system in the representation space and, as quantum states possess a minimum uncertainty, they minimize an invariant dispersion of the quadratic Casimir operator.
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