Accelerating Solitons

TL;DR

This paper develops a saddle-point approximation method for the effective Hamiltonian of quantum kinks in two-dimensional sigma models, enabling semiclassical calculations of soliton form factors at various momentum transfers.

Contribution

It introduces a novel saddle-point approximation for the effective Hamiltonian of quantum solitons, applicable to all orders in the time-derivative expansion, and derives explicit formulas for form factors.

Findings

Effective Hamiltonian reduces to H = (P^2 + M^2)^(1/2) at small momentum transfer.

Soliton form factors are expressed via Fourier transforms of classical profiles.

Method provides a systematic way to compute quantum corrections to soliton properties.

Abstract

We present the saddle-point approximation for the effective Hamiltonian of the quantum kink in two-dimensional linear sigma models to all orders in the time-derivative expansion. We show how the effective Hamiltonian can be used to obtain semiclassical soliton form factors, valid at momentum transfers of order the soliton mass. Explicit results, however, hinge on finding an explicit solution to a new wave-like partial differential equation, with a time-dependent velocity and a forcing term that depend on the solution. In the limit of small momentum transfer, the effective Hamiltonian reduces to the expected form, namely H = (P^2 + M^2)^(1/2), where M is the one-loop corrected soliton mass, and soliton form factors are given in terms of Fourier transforms of the corresponding classical profiles.