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Elimination des constantes arbitraires dans la théorie relativiste des quanta

Published inHelvetica physica acta, vol. 24, no. 2, p. 153-174
Publication date1951
Abstract

This article shows how the influence of the undetermined constants in the integral theory of collisions can be avoided. A rule is given by which the probability amplitudes (S[V]-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 Tomonaga, Schwinger, Feynman and Dyson in that the two sorts of diverging terms occuring in the formal solution of a Schroedinger equation are avoided. These two divergencies are: 1) the well known «self energy» divergencies which have been since corrected by methods of regularization (Rivier), Pauli and Villars; 2) the more serious boundary divergencies (Stueckelberg) 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-Retherford shift) obtained by Schwinger are, in the present theory, the boundary independent amplitudes in fourth approximation. Up to this approximation the rule eliminates the arbitrary constants from all conservative processes. § 1. contains an outline of the physical meaning of boundary effects. These effects involve a classical field which describes the actions of the counters necessary to distinguish between the incoming and outgoing particles. In § 2. the rule is formulated. It is based upon the unitarity and causality conditions developed in previous publications. In § 3. the limiting process is given which avoids the influences of the boundary. In particular, the limiting process necessary to apply the results to zero mass photons is given. § 4., § 5. and § 6. contain the application of the rule to the second, third, and fourth approximations of quantum electrodynamics for finite mass photons. It is shown that a certain ambiguity, related to charge renormalization, occuring in the work of Schwinger and Dyson is avoided if the explicit influence of the boundary region is taken into account.

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Citation (ISO format)
STUECKELBERG VON BREIDENBACH, Ernst Carl Gerlach, GREEN, Thomas Allen. Elimination des constantes arbitraires dans la théorie relativiste des quanta. In: Helvetica physica acta, 1951, vol. 24, n° 2, p. 153–174. doi: 10.5169/seals-112211
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ISSN of the journal0018-0238
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