Admissible Solutions of the Covariant Two-Body Problem

Abstract

The spectrum of Wick's two-body problem is examined with respect to normalization conditions and the assumptions made in deriving the equation. The problem is considerably simplified by using a formalism based on Sakata-Taketani field operators. It is found that the spurious state amplitudes (suitably normalized) have a behavior inconsistent with the assumptions used by Gell-Mann and Low to derive the boundstate equation. Similar results are found for the two-fermion problem if the vertex operator is ($1+{\gamma }_5$), and it is suggested that all spectra of the Bethe-Salpeter equation contain only three quantum numbers.