Summary
The method of Amati, Jengo and Remiddi for obtaining dispersion sum rules from current algebia is analysed in some detail, for the simple case of amplitudes connecting one particle and two currents. A simple perturbation-theory model provides a warning that the assumptions made in the derivation of the sum rules may not always be valid. When they are valid they may be used to give a derivation of the sum rules that is more direct that the one using current algebra.
Riassunto
Si esamina dettagliatamente il metodo di Amati, Jengo e Remiddi per ottenere regole di somma di dispersione dell’algebra delle correnti, nel caso semplice di ampiezze che connettono una particella a due correnti. Un semplice modello della teoria delle perturbazioni dà un avvertimento che le ipotesi fatte per dedurre le regole di somma possono non essere sempre valide. Quando sono valide possono essere usate per dare una deduzione delle regole di somma più diretta di quella che usa l’algebra delle correnti.
Резюме
Несколько подробно анализирется метод Амати, Дженго и Ремидди для получения дисперсионных, правил сумм из алгебры токов для простого случая, связывающего одну частицу и два тока. Простая модель теории возмущений предусматривает предупреждение, что предположения, сделанные при выводе правил сумм, невсегда могут быть обоснованы. Когда она справедливы, то они могут быть использованы для вывода правил сумм, что является более ясным, чем использование алгебры токов.
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References
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See alsoM. O. Taha: Cambridge preprints.
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The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research under Grant AF EOAR 65-36 through the European Office of Aerospace Research (OAR), United States Air Force.
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Halliday, I.G., Landshoff, P.V. Fubini sum rules for vertex functions. Nuovo Cimento A (1965-1970) 51, 980–998 (1967). https://doi.org/10.1007/BF02721767
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DOI: https://doi.org/10.1007/BF02721767