Quantum Properties of Solitons in $U(\phi)=\phi^2\ln^2(\phi^2)$ and $U(\phi)=\phi^2\cos^2(\phi^2)$ Models

TL;DR

This paper investigates the quantum properties of solitons in two newly constructed scalar field models, analyzing quantum corrections, meson scattering, and soliton mass calculations to deepen understanding of their quantum behavior.

Contribution

It introduces two new scalar field models with solitonic solutions and provides exact quantum corrections and mass evaluations, advancing the quantum analysis of solitons.

Findings

Quantum corrections are exactly solvable via Schrödinger equations.

Meson scattering by quantum solitons is analyzed at order .

Finite expressions for soliton masses are derived and approximated.

Abstract

Recently we constructed two new $(1+1)$-dimensional scalar field theory models that posses solitonic solutions. They are the $U(\phi)=\phi^2\ln^2(\phi^2)$ and the $U(\phi)=\phi^2\cos^2(\phi^2)$ models . The first quantum corrections for these models are given by exactly solvable Schrodinger equations. In this paper we first examine the quantum meaning of the solitonic solutions and study the scattering of the mesons by the quantum soliton at order $\hbar$. Finally we give a finite expression for the soliton masses of both models and evaluate such expression approximately in the case of the second model.