Two fermion relativistic bound states

Details Two fermion relativistic bound states Two fermion relativistic bound states

2004-05-29

arxiv.org/abs/hep-th/0405272v4

J.Phys. A38 (2005) 1345-1370

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, 6 figures

Scientific paper

10.1088/0305-4470/38/6/012

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.

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