Elliptically oscillating solutions in Abelian-Higgs model and electromagnetic property

TL;DR

This paper presents new elliptically oscillating solutions in the Abelian-Higgs model, deriving a massive dispersion relation from non-linear dynamics and exploring the electromagnetic properties of these solutions.

Contribution

It introduces novel elliptically oscillating solutions in the Abelian-Higgs model and derives their associated massive dispersion relation from the equations of motion.

Findings

Derived a new massive dispersion relation including scalar field value.

Analyzed the properties of the new solutions and their Hamiltonian density.

Established relations between scalar field value, electric field, and current-density.

Abstract

The elliptically oscillating solutions in the Abelian Higgs-model are presented and the classical massive-dispersion-relation through the non-linear dynamics is discussed. The generated massive-dispersion-relation including a field value of the scalar field is derived as the consequence of the equation of motions. We discuss the property of the new solutions and its Hamiltonian density. In addition, we calculate the electromagnetic property of the system, in particular, we derive the relation between the field value and the electric field and the electric current-density.