Feynman-Vernon model of a moving thermal environment

The formulation of the Feynman-Vernon model of linear dissipative systems, taking into account space and time invariance properties of a thermal environment, is reviewed. In this formulation the classical limit is consistently recovered and no infinite quantities appear at any step of the calculations. The model easily lends itself to be generalized to other types of environments. The case of a thermal environment moving with a time-dependent velocity with respect to the laboratory frame is studied. The corresponding classical Langevin equation and the influence functional of the quantum path integral formulation are derived.