Summary
Using scalar field theories as illustrative models, we elaborate on a previous proposal for rendering amplitudes in perturbation theory manifestly finite by expanding in terms of propagators of perturbed dimensions. We first considerρ 4, then we apply our scheme toρ 6 and, finally, we comment on the general case ofρ n,n≥4 and even. As in the usual approach to perturbation theory, we observe deviations from naive scaling of the amplitudes. But in this scheme, these deviations are due to the nonnaive scaling behavior of the momentum variables.
Riassunto
Per mezzo delle teorie di campo scalare come modelli illustrativi, si elabora una precedente idea per rendere le ampiezze in teoria delle perturbazioni manifestamente finite sviluppandole in termini di propagatori di dimensioni perturbate. Si considera dapprima la teoriaρ 4, poi si applica lo schema aρ 6 e infine si commenta il caso generale diρ n,n≥4 e pari. Come nell'approccio usuale alla teoria delle perturbazioni, si osservano deviazioni dalla semplice variazione di scala delle ampiezze. Ma in questo schema queste deviazioni sono dovute al comportamento non semplice della variazione di scala delle variabili dell'impulso.
Резюме
Используя теории скалярного поля как иллюстративные модели, мы выписаваем амплитуды в рамках теории возмущений. Сначала мы рассматриваемρ 4, затем применяем наму схему кρ 6 и, в заключение, мы анализируем общий случайρ n, гдеn является четным иn≥4. Как в обычном подходе теории возмущений, мы наблюдаем отклонения от скейлинга амплитуд. Но в этой схеме, эти отклонения обусловлены особым поведением скейлинга для импульсных переменных.
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Work supported in part by the U.S. Department of Energy under Contract Number EY-76-C-02-3065.
Traduzione a cura della Redazione.
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Mtingwa, S.K. Are nonrenormalizable theories really unrenormalizable?. Nuov Cim A 46, 605–621 (1978). https://doi.org/10.1007/BF02776975
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DOI: https://doi.org/10.1007/BF02776975