A Solvable Composite System in Relativistic Quantum Mechanics

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Abstract
The solvable two-body model in one space dimension proposed by Glöckle, Nogami and Fukui is reexamined. We find that their model is rewritten in a manifestly covariant form of Bethe-Salpeter equation with the Fermi-type interaction, provided that the single-electron-theoretical treatment is adopted. Owing to the ambiguities in the Dirac equation with delta function potential, we get eigenvalues for the mass of composite system different from theirs. We also treat the same model positron-theoretically and find that all the bound states in the single-electron-theoretical treatment disappear because of the pair effects to the delta function potential.

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