On Applications of theλ-Limiting Process to the Theory of the Meson Field

The $\lambda$-limiting process introduced by Wentzel and Dirac for the interaction of an electron with an electromagnetic field is applied to the interaction of a heavy particle (nucleon) with the meson field. One obtains in this way a more precise and relativistically invariant form of the theory which, in its classical interpretation, avoids all divergences of point sources. It is shown that the pseudoscalar and vector theories with a coupling constant $f$ of the dimension of length have in this form the character of a weak coupling theory with no stable isobars existing for $\mu f\ll 1$. The higher approximations for the interactions between nucleons are investigated for the example of a Rosenfeld-Møller mixture with the results that they are finite as long as the nucleons are treated to be at rest and small in comparison with the $f^2$ approximation for distances of the nucleons from each other sufficiently larger than $f$.