A symmetry breaking mechanism for selecting the speed of relativistic solitons

TL;DR

This paper introduces a novel mechanism to control the velocity of relativistic sine-Gordon solitons by breaking Lorentz symmetry, applicable to molecular chains and broader field theories, while maintaining soliton stability.

Contribution

It presents a new symmetry breaking approach to fix soliton speeds in sine-Gordon models, extending from molecular chains to general two-dimensional field theories.

Findings

Mechanism allows tuning soliton speed via elastic parameters.

Relativistic features like topological charge and stability are preserved.

Applicable to both molecular models and field theories.

Abstract

We propose a mechanism for fixing the velocity of relativistic soliton based on the breaking of the Lorentz symmetry of the sine-Gordon (SG) model. The proposal is first elaborated for a molecular chain model, as the simple pendulum limit of a double pendulums chain. It is then generalized to a full class of two-dimensional field theories of the sine-Gordon type. From a phenomenological point of view, the mechanism allows one to select the speed of a SG soliton just by tuning elastic couplings constants and kinematical parameters. From a fundamental, field-theoretical point of view we show that the characterizing features of relativistic SG solitons (existence of conserved topological charges and stability) may be still preserved even if the Lorentz symmetry is broken and a soliton of a given speed is selected.