Perturbation expansion around extended-particle states in quantum field theory

Abstract

The quantum mechanics of solitary-wave classical solutions of nonlinear wave equations is discussed in detail for the kink solution of two-dimensional ${\ensuremath{\varphi}}^{4}$ field theory. The formalism provides a natural interpretation of an extended particle, the soliton, for the classical kink. The perturbation theory around the extended particle is developed and used to calculate the radiative corrections for the mass of soliton up to one loop. The mass renormalization is discussed in detail to show that the mass counterterm to the nonsoliton sector also does the job for the present case, i.e. one-soliton sector. Although our formalism is not manifestly Lorentz-covariant, the Lorentz covariance is shown explicitly by calculating the soliton energy for a fixed momentum. The paper also contains the perturbation calculation of matrix element of $\ensuremath{\varphi}$ fields between one-soliton states.