Elimination des constantes arbitraires dans la theorie relativiste des quanta [85]

Summary

This article shows how the influence of the undetermined constants in the integral theory of collisions¹)²)³)⁴) can be avoided. A rule is given by which the probability amplitudes (5[F]-matrix) may be calculated in terms of a given local action. The procedure of the integral method differs essentially from the differential method employed by Tomonaga⁶), Schwikger⁵), FÅÕímaí7) and Dyson⁸) in that the two sorts of diverging terms occuring in the formal solution of a Schroedinqer equation are avoided. These two divergencies are: 1) the well known «.self energy» divergencies which have been since corrected by methods of regularization (Rivikr¹), Pattli and Villaks⁹)); 2) the more serious boundary divergencies (Stueckelberg⁴)) due to the sharp spatio-temporal limitation of the space-time region of evolution V in which the collisions occur. The convergent parts (anomalous g-factor of the electron and the Lamb-Rethekford shift) obtained by Schwinger are, in the present theory, the boundary independent amplitudes in fourth approximation. Üp to this approximation the rule eliminates the arbitrary constants from all conservative processes.