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Hochenergieverhalten von Streuamplituden in der Störungstheorie und im multiperipheren Modell
Author(s) -
Sommer G.
Publication year - 1964
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19640121202
Subject(s) - fubini's theorem , scattering amplitude , logarithm , amplitude , perturbation theory (quantum mechanics) , physics , mathematical physics , coupling (piping) , mathematics , scattering , quantum electrodynamics , mathematical analysis , quantum mechanics , mechanical engineering , engineering
A review is given of theorems and models for the high energy behaviour of scattering amplitudes. Furthermore it is shown that the scattering amplitude at extremely high energies cannot be approximated only by the sum of ladder graphs. By substitution of some of the ladder “rungs” by special subgraphs, we find after summing up a scattering amplitude asymptotically larger than the original one. Especially, the sum of all “ladder diagrams with two crossed rungs” exceeds the ladder approximation of the Bethe‐Salpeter equation by a factor proportional to the logarithm of the energy. This result is true as well in perturbation theory for A 3 ‐coupling as in the framework of the Amati‐Fubini‐Stanghellini model. As a consequence asymptotically the total cross section in the multiperipheral model is not given by the imaginary part of the sum of ladder graphs, but all permutations of the multiperipherically produced particles are important at high energies.