Relativistic k-fields with Massless Soliton Solutions in 3+1 Dimensions

TL;DR

This paper introduces a new relativistic k-field model in 3+1 dimensions that admits a unique, energetically stable, massless non-topological solitary wave solution, expanding the understanding of stable massless solitons.

Contribution

The work presents a novel 3+1 dimensional k-field model with a stable, massless soliton solution, which was not previously known.

Findings

A new stable, massless soliton solution in 3+1 dimensions.

The solution has zero total energy, indicating stability.

The model broadens the class of stable, massless solutions in relativistic field theories.

Abstract

In this work, the relativistic non-standard Lagrangian densities (k-fields) with massless solutions are generally introduced. Such solutions are not necessarily energetically stable. However, in 3+1 dimensions, we introduce a new k-field model that results in a single non-topological massless solitary wave solution. This special solution is energetically stable; that is, any arbitrary deformation above its background leads to an increase in the total energy. In other words, its energy is zero which is the least energy in all solutions. Hence, it can be called a massless soliton solution.