Three Field Dynamics in (1+1)-dimensions

TL;DR

This paper investigates the dynamics of a massive particle in a (1+1)-dimensional nonlinear scalar field model with Higgs-like potentials, revealing barrier and scattering solutions influenced by the Higgs condensate.

Contribution

It introduces a novel (1+1)-dimensional model with anti-Higgs and Higgs potentials and analyzes the particle dynamics within this framework.

Findings

Effective potential forms a two-hump barrier in spacetime.

Particle can be captured or scattered by the potential barrier.

Asymptotic potential approaches a constant determined by the Higgs condensate.

Abstract

In a model of nonlinear system of three scalar fields the problem on dynamics of a massive particle moving in effective potential provided by two relativistic fields is solving. The potentials for these fields are chosen in the form of anti-Higgs and Higgs potentials. It is shown that the effective potential has the shape of two-hump barrier localized in spacetime. It tends to constant attractive potential at spacetime infinity. The magnitude of this constant constituent is determined by the Higgs condensate. It is shown that nonlinear equation of motion of a particle has the solutions which describe the capture of a particle by the barrier and the scattering on the barrier.