An SL(2,C)-invariant representation of the Dirac equation. II. Coulomb Green’s function

Abstract

The Kepler problem for the Klein–Gordon type wave equation {ΠμΠμ+m2+ieσ⋅(ℰ+iB)}φ=0, investigated earlier [J. Math. Phys. 23, 1179 (1982)] and proven to be equivalent to the conventional Dirac equation, is discussed. In this equation φ is a 2×1 Pauli spinor and σa, a=1, 2, 3, are the usual 2×2 Pauli spin matrices. Quite simple expressions for the bound state Coulomb wavefunctions and for the Coulomb Green’s function are obtained by exploiting the concept of ‘‘coupling constant eigenfunction.’’ To facilitate the direct use of these simple expressions in Coulomb calculations, a stationary state perturbation theory appropriate for the Klein–Gordon type wave equation itself is described.