Summary
Feynman’s method for the integration on internal momenta in Feynman’s amplitudes with the use of auxiliary variables, is extended so as to perform the integration on the final external momenta, in the expressions for total cross-sections. After integration on the final momenta, covariant integral representations are obtained for total cross-sections, in which the integrands exhibit a simple energy-dependence, while the variable limits are completely indipendent of kinematics. It is argued that such expressions may be suitable to extract the dominant parts of total cross-sections in the high-energy limit. In this connection, two simple examples are given.
Riassunto
Il metodo di Feynman per integrare sui quadrivettori interni nelle ampiezze di Feynman con l’uso di variabili ausiliarie, è esteso ai quadrivettori esterni. Dopo l’inte-grazione sui momenti finali, si ottengono per le sezioni d’urto totali, rappresentazioni integrali covarianti, nelle quali gli integrandi esibiscono una semplice dipendenza dalla energia; inoltre, i limiti per le variabili sono indipendenti dalla cinematica. Si arguisce che tali rappresentazioni possono essere utili per estrarre la parte asintotica delle sezioni d’urto totali per alte energie. A questo riguardo si danno due semplici esempi.
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Cazzola, P. Total cross-sections in perturbation theory in the high-energy limit. Nuovo Cim 34, 221–235 (1964). https://doi.org/10.1007/BF02725882
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DOI: https://doi.org/10.1007/BF02725882