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By using the overcompleteness of coherent states we find an alternative formof the unit operator for which the ket and the bra appearing under theintegration sign do not refer to the same phase-space point. This defines a newquantum representation in terms of Bargmann functions, whose basic features arepresented. A continuous family of secondary reproducing kernels for theBargmann functions is obtained, showing that this quantity is not necessarilyunique for representations based on overcomplete sets. We illustrate theapplicability of the presented results by deriving a semiclassical expressionfor the Feynman propagator that generalizes the well-known van Vleck formulaand seems to point a way to cope with long-standing problems in semiclassicalpropagation of localized states.

Off-center coherent-state representation and an application to semiclassics