Coherent Schwinger Interaction from Darboux Transformation

TL;DR

This paper derives exactly solvable potentials for the Dirac equation using Darboux transformations, revealing insights into Schwinger interactions and nucleon-channeling phenomena in a novel analytical framework.

Contribution

It introduces a new method to construct scalar-tensor potentials for the Dirac equation via Darboux transformations, linking them to Schwinger interactions.

Findings

Exact scalar-tensor potentials derived for Dirac equation

Analytic structure of Lyapunov functions analyzed

Connection established between Darboux transformations and Schwinger interactions

Abstract

The exactly solvable scalar-tensor potential of the four-component Dirac equation has been obtained by the Darboux transformation method. The constructed potential has been interpreted in terms of nucleon-nucleon and Schwinger interactions of neutral particles with lattice sites during their channeling Hamiltonians of a Schwinger type is obtained by means of the Darboux transformation chain. The analitic structure of the Lyapunov function of periodic continuation for each of the Hamiltonians of the family is considered.