Solution of Relativistic Feshbach-Villars Spin-1/2 Equations

TL;DR

This paper introduces a novel method for analyzing relativistic spin-1/2 particles using Feshbach-Villars equations, reformulating them as coupled spin-0 equations and solving via an integral equation approach.

Contribution

It presents a new formulation of Feshbach-Villars spin-1/2 equations as coupled spin-0 equations and applies an integral equation method with matrix continued fractions.

Findings

Reformulation as spin-coupled equations simplifies the problem.

Green's operator computed via matrix continued fraction.

Method enables solving relativistic spin-1/2 equations efficiently.

Abstract

We propose method for studying relativistic spin-$1/2$ particles by solving the corresponding Feshbach-Villars equation. We have found that the Feshbach-Villars spin-$1/2$ equations can be formulated as spin-coupled Feshbach-Villars spin-$0$ equations, that results in a Hamiltonian eigenvalue problem. We adopted an integral equation formalism. The potential operators are represented in a discrete Hilbert space basis and the relevant Green's operator has been calculated by a matrix continued fraction.