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Abstract
We have studied four possible Green's functions of the Bethe-Salpeter equation for equal mass scalar bosons by considering contours in an off-the-mass-shell complex energy (Ω) plane and an on-the-mass-shell magnitude of 3-momenta (k) or energy (ωk) complex plane. We find that three of the Green's functions—causal, retarded, and advanced Green's function—cannot lead to scattering solutions. Only a new Green's function, which we have called the scattering Green's function, with appropriate restrictions on the interaction V(x), can lead to scattering states.
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