Relativistically Invariant Description of Fluctuations Against the Background of Classical Kink Solutions

TL;DR

This paper develops a relativistically invariant framework to describe fluctuations around classical kink solutions, identifying normal modes and deriving a Hamiltonian for excitations.

Contribution

It introduces a novel relativistically invariant scheme for analyzing excited states in a kink background, automatically excludes zero modes, and formulates a Hamiltonian for elementary excitations.

Findings

Normal oscillations are determined against a moving kink background.

Zero mode of fluctuations is automatically excluded.

A Hamiltonian reflecting relativistic properties is derived.

Abstract

A relativistically invariant scheme for the description of excited states in a one-kink sector is formulated. The normal oscillations of fluctuations against the background of a moving kink are determined. Zero mode of these oscillations is excluded automatically due to the properties of the integral equation describing normal oscillations. A Hamiltonian for elementary excitations is obtained reflecting the relativistic nature of the problem considered. (35 kb)