Quantum expansion of soliton solutions

Abstract

A systematic quantum expansion of soliton solutions to nonlinear field equations is developed. The method is based on the standard canonical quantization procedure. When the nonlinear coupling $O\left(g^{-2\mathrm{}}\right)$ is small, the Hamiltonian is $g$ and its quantum eigenstates take on a WKB form, giving a direct connection between the quantum description and the corresponding classical soliton solution (which can be in any dimension, either time-dependent or time-independent). Our general method is illustrated by a variety of one-space-dimensional examples, some new and some old.