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Reduction of feynman diagrams | Il Nuovo Cimento A (1965-1970)

Formulae expressing the amplitude for a Feynman diagram consisting of a single internal loop withn sides andn external lines as a sum of its reduced diagrams are derived by applying restrictions imposed by the finite dimensionality of space-time on the unparametrized amplitude. In 4-dimensional space-time these formulae express the amplitude for then-sided diagram as i) a sum of all its 5-sided reduced diagrams; this can be further expressed as ii) a sum of all its 4-sided reduced diagrams. The coefficients in each sum depend only on the external invariants and internal masses.

Applicando le restrizioni imposte alla ampiezza non parametrizzata dalla dimensionalità finita dello spazio-tempo, si deducono le formule che esprimono l'ampiezza di un diagramma di Feynman composto di un solo nodo interno conn lati edn linee esterne come somma dei suoi diagrammi ridotti. Nello spazio-tempo quadridimensionale queste formule esprimono l'ampiezza dei diagrammi conn lati come i) una somma dei loro diagrammi ridotti con 5 lati; questi possono essere inoltre espressi come ii) una somma di tutti i loro diagrammi ridotti con 4 lati. I coefficienti di ciascuna somma dipendono solo dagli invarianti esterni e dalle masse interne.

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1. D. B. Melrose

   Present address: Department of Physics, University of Sussex, Brighton, UK

1. Clarendon Laboratory, Department of Theoretical Physics, Oxford, UK

   D. B. Melrose

Traduzione a cura della Redazione.

Melrose, D.B. Reduction of feynman diagrams. Nuovo Cimento A (1965-1970) 40, 181–213 (1965). https://doi.org/10.1007/BF02832919

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• Received: 19 May 1965

• Published: 01 November 1965

• Issue Date: November 1965

• DOI: https://doi.org/10.1007/BF02832919

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