A Solution of the Relativistic Schr\"odinger Equation for the $\delta$-Function Potential in 1-dimensiona with Cutoff Regularization

TL;DR

This paper solves the relativistic Schrödinger equation with a delta-function potential in one dimension using cutoff regularization, demonstrating renormalizability and equivalence with dimensional regularization results.

Contribution

It introduces cutoff regularization to solve the relativistic Schrödinger equation with delta potential, establishing renormalizability and equivalence with dimensional regularization.

Findings

The problem is renormalizable.

Results match those from dimensional regularization.

Regularization method is effective for this problem.

Abstract

We study the solution of the relativistic Schr\"odinger equation for a point particle in 1-d under $\delta$-function potential by using cutoff regularization. We show that the problem is renormalizable, and the results are exactly the same as the ones obtained using dimensional regularization.