Solitary waves in Galilean covariant Fermi field theories with self-interaction

TL;DR

This paper constructs spin-up solitary wave solutions in a generalized Levy-Leblond equation for a self-interacting Fermi field, revealing mass discrepancies between inertial and rest masses in a Galilean covariant framework.

Contribution

It introduces new solitary wave solutions in a self-interacting Fermi field theory within a Galilean covariant setting, highlighting mass accumulation phenomena.

Findings

Existence of spin-up solitary wave solutions with space oscillations

Solutions exhibit non-equal inertial and rest masses

Advances understanding of non-relativistic fermionic field theories

Abstract

The generalized Levy-Leblond equation for a $(3+1)$-dimensional self-interacting Fermi field is considered. Spin up solitary wave solutions with space oscillations in the $x^3$-coordinate are constructed. The solutions are shown to accumulate non-equal amounts of inertial and rest masses.