Darboux Transformation of the Green Function for the Dirac Equation with the Generalized Potential

We consider the Darboux transformation of the Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We obtained the Green functions of the transformed Dirac equation with the initial regular boundary conditions. We also construct the formula for the unabridged trace of the difference of the transformed and the initial Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We illustrate our findings by the consideration of the Darboux transformation for the Green function of the free particle Dirac equation on an interval.