Confinement limit of Dirac particles in scalar 1D potentials

TL;DR

This paper proves that Dirac particles cannot be confined below their Compton wavelength using scalar potentials, regardless of potential symmetry or nonlinearity, and discusses potential physical realizations.

Contribution

It provides a general, Heisenberg-independent proof of the confinement limit for Dirac particles in scalar potentials and extends applicability to nonlinear interactions.

Findings

Dirac particles cannot be localized below their Compton length

The proof applies to symmetric and arbitrary scalar potentials

Potential real-world systems are proposed for realization

Abstract

We present a general proof that Dirac particles cannot be localized below their Compton length by symmetric but otherwise arbitrary scalar potentials. This proof does not invoke the Heisenberg uncertainty relation and thus does not rely on the nonrelativistic linear momentum relation. Further it is argued that the result is also applicable for more general potentials, as e.g. generated by nonlinear interactions. Finally a possible realisation of such a system is proposed.