Effective dipole-radiation-field theory: III. Three-dimensional oscillator
TNO Fysisch en Elektronisch Laboratorium
The novel analysis of the interaction between a harmonically bound, nonrelativistic "isotropic point" charge and the electromagnetic field as presented in paper I [Int. J. Mod. Phys. B8, 2307 (1994)] and II [Int. J. Mod. Phys. B10, 1211 (1996)], is finally extended to the case of a three-dimensional oscillator. The coupling between the electron and the field is treated through all orders beyond the standard dipole model. After a statistical linearization of the highly nonlinear dynamics, the problem is solved exactly in terms of the system's normal modes. The procedure intrinsically involves a generalized mass renormalization. The solution is free of runaway modes. The quantum mechanical ultraviolet divergence known from the standard dipole model is shown to be suppressed by the generalized coupling. Inter alia an effective equation of motion for the charge is derived. It is also shown that the zero-coupling and the infinite-system limits do not commute.
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International Journal of Modern Physics B, 12 (9), 965-987