Abstract
Coherent states on the m-sheeted complex plane are introduced and properties like overcompleteness and resolution of the identity are studied. Operators am+, am which create and annihilate clusters of m particles are considered and it is shown that the properties of our coherent states with respect to them are analogous to the properties of the ordinary (Glauber) coherent states with respect to a+, a. An extended Bargmann representation in the m-sheeted complex plane and P and Q representations with respect to our coherent states, are studied. Applications of this formalism in the study of Hamiltonians that describe m-particle clustering are also considered.
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