Energy corrections and persistent perturbation effects in continuous spectra

Abstract

The quantum-mechanical perturbation theory of continuous energy spectra is investigated for a special class of perturbations possessing some of the formal properties of the familiar interaction energies of field theory. These formal properties entail the inapplicability of the familiar perturbation theory of continuous spectra. The latter, which implies that the perturbation causes transitions between unperturbed stationary states, with conservation of the unperturbed energy, is valid for scattering and reaction processes. The perturbations here considered are found to produce transitions between “asymptotically stationary states” differing from the unperturbed stationary states both by the admixture of other states and by correction of the energy value. This is in agreement with the situation intuitively expected but not explicitly verified in field theory (due to divergence and computational difficulties), according to which the interaction between fields causes, besides scattering, creation or annihilation processes, the persistent occurrence around each real particle of a cloud of virtual particles (photon cloud around an electron, meson cloud around a nucleon, etc.), with an accompanying self-energy effect.