The modulated soliton fields in the Goldstone boson model

TL;DR

This paper presents exact solitonic solutions in the Goldstone boson model, revealing localized energy densities with a massive and a massless boson, and suggests potential experimental detection of Goldstone bosons.

Contribution

It provides the first exact solitonic solutions in the Goldstone boson model, demonstrating energy localization and wave modulation effects.

Findings

Existence of localized solitonic solutions with energy concentration.

Massless wave modulated and riding on a massive wave.

Calculated charge density confirms boson neutrality.

Abstract

It is well known that massless Goldstone bosons have not yet been observed. In the Goldstone boson model, after the spontaneous symmetry breaking under $U(1)$, two coupled nonlinear equations are obtained for which we present the exact solitonic solutions. These solutions completely localize the energy density of the model and show the existence of two boson fields, one massive and the other massless. Also, it is seen that the solitonic waves are modulated and the massless wave rides on the massive wave. Finally, we calculate the charge density of the model, which again confirms the neutrality of these boson fields. Since massive bosons can be observed in the laboratory, these solitonic waves may be useful in tracking and detecting Goldstone bosons.