Current conserving random phase approximation

The consequences of the continuity equation for the RPA are exploited, if charge and current densities are given. Simple, yet stringent conditions for the RPA amplitudes and the residual interaction are obtained. Under these conditions the RPA equations are simplified and exactly reduced to a hermitean eigenvalue problem of half the original dimensionality. Transition current matrix elements are then similar to those of an effective current recently proposed for TDA calculations.