Quadratic supersymmetric transformations of the Dirac Green functions

TL;DR

This paper explores quadratic supersymmetric transformations applied to the Green functions of the one-dimensional Dirac equation, deriving relations and formulas that connect initial and transformed functions, with an illustrative example.

Contribution

It introduces a novel quadratic supersymmetric approach to Dirac Green functions and derives explicit relations and trace formulas for transformed solutions.

Findings

Derived relations between initial and transformed Green functions.

Constructed a formula for the unabridged trace difference.

Provided an illustrative example demonstrating the method.

Abstract

We consider the quadratic supersymmetric aspect of the Darboux transformation for the Green functions of the one-dimensional Dirac equation with a generalized form of the potential. We obtain the relation between the initial and the transformed Green functions on the whole real line. We also construct the formula for the unabridged trace of the difference of the transformed and the initial Green functions of the boundary problem on the whole real line. We present an example illustrated our developments.