A New Form of Path Integral for the Coherent States Representation and its Semiclassical Limit L. C. dos Santos and M. A. M. de Aguiar Instituto de Fı́sica ‘Gleb Wataghin’

The overcompleteness of the coherent states basis leads to a multiplicity of representations of Feynman’s path integral. These different representations, although equivalent quantum mechanically, lead to different semiclas-sical limits. Two such semiclassical formulas were derived in [1] for the two corresponding path integral forms suggested by Klauder and Skagerstan in [2]. Each of these formulas involve trajectories governed by a different classical representation of the Hamiltonian operator: the P representation in one case and the Q representation in other. In this paper we construct a third representation of the path integral whose semiclassical limit involves directly the Weyl representation of the Hamiltonian operator, i.e., the classical Hamiltonian itself.