Two fermion relativistic bound states

Abstract

We consider the relativistic quantum mechanics of a two interacting fermions system. We first present a covariant formulation of the kinematics of the problem and give a short outline of the classical results. We then quantize the system with a general interaction potential and deduce the explicit equations in a spherical basis. The case of the Coulomb interaction is studied in detail by numerical methods, solving the eigenvalue problem for J=0, J=1, J=2 and determining the spectral curves for a varying ratio of the mass of the interacting particles. Details of the computations, together with a perturbative approach in the mass ratio and an extended description of the ground states of the Para- and Orthopositronium are given in Appendix.

26 pages, 6 figures

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Cited by in corpus (7)

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• Two fermion relativistic bound states: hyperfine shifts
• Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction
• Relativistic two fermion treatment of hyperfine transitions
• Relativistic two-body calculation of $b\bar{b}$-mesons radiative decays