Normalization Condition and Normal and Abnormal Solutions of the Bethe-Salpeter Equation. II

The normalization integrals of the Bethe-Salpeter amplitudes are calculated in the Wick-Cutkosky model in order to check the conjecture that the sign of the norm is ${\mathrm{}(-1\mathrm{})\mathrm{}}^{\kappa }$ for $0<s<\mathrm{}4\mathrm{}$. It is explicitly verified for the following solutions with $n=l+1\mathrm{}$: (1) $\kappa$ arbitrary, $s$ infinitesimal; (2) $\kappa =0\mathrm{}$, $0<s\le 2$; (3) $\kappa =1\mathrm{}$, $0<s\le 2+{\mathrm{}(n+2\mathrm{})\mathrm{}}^{-1\mathrm{}}$; (4) $\kappa =0\mathrm{}$, $4-s$ infinitesimal. Here $\kappa$, $n$, $l$ are the conventional quantum numbers, and $s^{\frac{1}{2}}$ denotes the bound-state mass in units of the constituent-particle mass. Some speculations are presented concerning the existence of ghost states.