Resolving an interface problem for the Dirac equation by using the unified transform method

TL;DR

This paper applies the Unified Transform Method to solve interface problems for the Dirac equation across various domain configurations, providing explicit integral solutions.

Contribution

It extends the UTM to vector cases of the Dirac equation, offering convergent integral representations for complex domain interface problems.

Findings

Explicit integral solutions for Dirac interface problems.

Extension of UTM to vector Dirac equations.

Convergent solutions on multiple domain types.

Abstract

We use the Unified Transform Method (UTM) for the vector case to resolve an interface problem for the Dirac equation on two semi-infinite domains and two finite domains in the massless and massive cases, respectively. The UTM for the vector case is a variation of the UTM for the scalar case. The solutions obtained for an interface problem on two semi-infinite domains and two finite domains, respectively, in the massive case are convergent explicit integral representations.