Fermion Number Fractionization

TL;DR

This paper discusses the phenomenon of fermion number fractionization associated with solitons in non-linear wave equations, highlighting its discovery and implications in organic conductors like polyacetylene chains.

Contribution

It explains the emergence of fractional fermion numbers in soliton solutions of the Dirac equation and their significance in the development of organic conductors.

Findings

Fermion number can be fractional in soliton backgrounds.

Solitons in polyacetylene chains exhibit fractional fermion numbers.

This phenomenon contributed to advances in organic conductor technology.

Abstract

Solitons emerge as non-perturbative solutions of non-linear wave equations in classical and quantum theories. These are non-dispersive and localised packets of energy-remarkable properties for solutions of non-linear differential equations. In presence of such objects, the solutions of Dirac equation lead to the curious phenomenon of "fractional fermion number", a number which under normal conditions takes strictly integral values. In this article, we describe this accidental discovery and its manifestation in polyacetylene chains, which has lead to the development of organic conductors.