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

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.