Coherent State Path Integrals in the Weyl Representation

Details Coherent State Path Integrals in the Weyl Representation Coherent State Path Integrals in the Weyl Representation

2006-07-20

arxiv.org/abs/quant-ph/0607136v1

J. Phys. A: Math. Gen. 39 (2006) 13465-13482.

Physics

Quantum Physics

23 pages

Scientific paper

10.1088/0305-4470/39/43/006

We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in \cite{Klau85}, which involve the normal or the antinormal ordering of the Hamiltonian. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. We show that the semiclassical limit of the coherent state propagator in Weyl representation is involves classical trajectories that are independent on the coherent states width. This propagator is also free from the phase corrections found in \cite{Bar01} for the two Klauder forms and provides an explicit connection between the Wigner and the Husimi representations of the evolution operator.

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