  Recently, it is shown that the extended phase space formulation of quantum
mechanics is a suitable technique for studying the quantum dissipative systems.
Here, as a further application of this formalism, we consider a dissipative
system of charged particles interacting with an external time dependent
electric field. Such a system has been investigated by Buch and Denman, and two
distinct solutions with completely different structure have been obtained for
Schr\"odinger's equation in two different gauges. However, by generalizing the
gauge transformations to the phase space and using the extended phase space
technique to study the same system, we demonstrate how both gauges lead to the
same conductivity, suggesting the recovery of gauge invariance for this
physical quantity within the extended phase space approach.
