MEAN FIELDS - EXPLICIT DISPERSIVE AND RETARDATION PROPERTIES OF THE DYNAMICAL POLARIZATION POTENTIAL WITHIN A SIMPLE-MODEL

The dynamical polarization potential corresponding to a simple and tractable, but physically meaningful, two-channel model is derived and examined, with particular attention to its analytic properties. This enables us to illustrate explicitly the emergence of the general dispersive and retardation features expected from the imposition of causality. The energy dependence of the potential, and the associated nonlocality in time expressed by its Fourier transform, are explored. A new theorem is proposed for the asymptotic behavior of the Fourier transforms.