Time dependence of the field energy densities surrounding sources: Application to scalar mesons near point sources and to electromagnetic fields near molecules

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Abstract
The time dependence of the dressing-undressing process, i.e., the acquiring or losing by a source of a boson field intensity and hence of a field energy density in its neighborhood, is considered by examining some simple soluble models. First, the loss of the virtual field is followed in time when a point source is suddenly decoupled from a neutral scalar meson field. Second, an initially bare point source acquires a virtual meson cloud as the coupling is switched on. The third example is that of an initially bare molecule interacting with the vacuum of the electromagnetic field to acquire a virtual photon cloud. In all three cases the dressing-undressing is shown to take place within an expanding sphere of radius r=ct centered at the source. At each point in space the energy density tends, for large times, to that of the ground state of the total system. Differences in the time dependence of the dressing between the massive scalar field and the massless electromagnetic field are discussed. The results are also briefly discussed in the light of Feinberg’s ideas on the nature of half-dressed states in quantum field theory.