Krakow Lectures on Scalar Quantum Solitons

TL;DR

This paper introduces Linearized Soliton Perturbation Theory (LSPT), a Hamiltonian-based method for quantum soliton calculations, focusing on state construction, corrections, and scattering analysis.

Contribution

It presents a new, efficient Hamiltonian approach for quantum solitons, including multi-loop corrections and an inner product for non-normalizable states.

Findings

Constructed soliton states as squeezed, coherent states with corrections

Calculated multi-loop corrections to soliton states and masses

Applied inner product to kink-meson scattering

Abstract

We give a pedagogical introduction to Linearized Soliton Perturbation Theory (LSPT), a new and efficient tool for calculations involving quantum solitons. It is a Hamiltonian approach with a focus on explicitly constructing the soliton states. These states are squeezed, coherent states plus perturbative corrections. We will describe multi-loop corrections to states and their masses. An inner product suitable for non-normalizable momentum eigenstates will be introduced and applied to kink-meson scattering. We will also discuss domain wall solitons.