Suchergebnisse

Defining generalised functions products by analytic continuation, a two-point function whose mass distribution is positive may be used in the non linear spinor theory. As an application, we show that in an approximation where only strong interactions are considered — so that no imaginary parts have to be neglected, correct values for the π and η meson masses (and eventually, using enough parameters, for the meson nucleon coupling constants) may be obtained, in the first order of the new Tamm-Dancoff method, if the mass distribution is positive ; if not, it seems that the contribution of the negative part must be negligible.

The L, M, N functions whose definition and analytical expression were given in the first part of this article are further examinated to give their behaviour for small λ values. The imaginary parts are calculated by a direct method and the simpler functions to which L, M, N reduce when µ equals unity (ξ = η) are graphically represented. Formula's numbers follow those of the first part whose results are not repeated.

Abstract. — In the non-linear theory of elementary particles by Heisenberg and coworkers new functions were introduced, which were called L, M, N by the authors. These functions which depend on two parameters, ξ, η are studied in the general case where ξ is different from η. We expose here the method leading to their analytical expressions.