Positive mass distribution in the non linear spinor theory

Abstract

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.