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The Bethe-Salpeter equation for nucleon-nucleon scattering is a singular integral equation, and it is therefore not certain that a unique solution exists. It is shown that the equation is soluble for states of all angular momentum, parity and isotopic spin if, and only if, g2/4π is less than 1/6π. The range of values of g for which there exist solutions of a particular angular momentum and parity is given. The Bethe-Salpeter equation for meson-nucleon scattering is also examined. In this case, the equation is soluble for all values of the coupling constant, but the solution, regarded as a function of g, will exhibit discontinuities when g passes through certain values.
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S. Mandelstam (1956) studied this question.
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