Possible equalities of the differential reaction cross sections for asymptotically large energies and transmitted impulses

Abstract

A connection is established between the asymptotic equivalence of the exact and asymptotic amplitudes introduced by Meiman, and the character of the behavior of the “effective space region σ of the interaction of particles” with high energy s and a fixed transmitted impulse t. The possibilities of obtaining equalities of the differential cross sections for both cross reactions (for any type of interaction) and for C-conjugate reactions (for C-noninvariant interactions) with asymptotically large s, t, and u simultaneously are investigated. It is shown that these equalities can be obtained on the basis of physically meaningful postulates of quantum field theory if specific limitations are imposed on the behavior of the “effective times σ⁰ and space regions σ of particle interactions” with asymptotically large s, t, and u. Among these postulates the basic formulation of Bogolyubov's principle of microcausality plays the greatest part. The experimental confirmation or otherwise of these asymptotic equalities could in this way give definite information concerning the asymptotic behavior of σ⁰ and σ which is completely lacking at the present time.