Dimensional Regularization of the Spatial wave function for a singular contact interaction in the Relativistic Schrodinger Equation

Abstract

Based on our previous work in PRD 89, 125023 (2014), we stress here (for the first time) the regularization of the spatial wave function for the δ-contact interaction within the relativistic Schrodinger equation. The D-dimensional inverse Fourier transform has been utilized to map the momentum-space wave function to the spatial one. To regularize the logarithmic blow up of the wave function as x → 0, we employed the dimensional regularization technique. We assert that although the technique has been used here for the bound state only, the form of the scattering states in momentum space assures the reliability of the same technique to regularize the spatial scattering wave functions.