Runaway Modes Research Articles

EFFECTIVE DIPOLE-RADIATION-FIELD THEORY I: ONE-DIMENSIONAL OSCILLATOR BEYOND STANDARD COUPLING

A novel generalization is given of the standard dipole interaction between a charged particle and the electromagnetic field in the radiation gauge. The resulting nonlinear interaction problem is statistically linearized. The ensuing dynamics is solved exactly for a harmonically bound nonrelativistic electron in a finite region of three-dimensional space. The solution involves a generalized renormalization procedure and is free of runaway modes. The theory is particularly suited for a self-consistent treatment of the system's quantum mechanics. As a consequence of the generalized coupling an earlier noted ultraviolet quantum mechanical divergence is absent.

Runaway Modes in Dipole Electrodynamics with Shadow States

Runaway Modes in Dipole Electrodynamics with Shadow States

Resolution of the Runaway Problem for the Polaron

Runaway modes are shown to result from the standard application of the dipole approximation to the polaron Hamiltonian. These modes do not occur if the Hamiltonian is renormalized before making the approximation.

Runaway Modes in Model Field Theories

Within the framework of linear quantum field theories, a general study is presented of the existence and removal of runaway modes---solutions of the equations of motion which exhibit a real exponential time dependence. It is hoped that this work will yield insight into the corresponding problem in physically realistic theories. It is shown that runaway modes occur only when the Hamiltonian is not positive definite, and that they occur in linear quantum theories whenever they appear in the corresponding classical theories. Three methods are proposed for eliminating these unphysical modes One is the analog of the method used by Dirac in classical electron theory; the other two are believed to be new.