Summary
Schwinger’s formula, (z+iɛ−1=−i∫ exp [ia(z+iɛ)] da, is applied to the propagators of Feynman diagrams. All the integrations over internal momenta are performed explicitly, leaving expressionswhich involve only the auxiliary parametersa n and the external momenta. It is shown how to modify these formulas so as to « switch off » adiabatically the interaction outside a given space-time domain. Possible applications of this method to the study of analyticity properties are briefly discussed.
Rassiunto
Si applica la formula di Schwinger, (z+iɛ−1=−i∫ exp [ia(z+iɛ)] da, ai propagatori dei diagrammi di Feynman. Si eseguono esplicitamente tutte le integrazioni sui momenti interni, ottenendo espressioni in cui compaiono solo i parajnetri ausiliaria n e i momenti esterni. Si mostra come modificare queste formule in modo da « spegnere » adiabaticamente l’interazione al di fuori di un dato dominio spazio-temporale. Si discutono brevemente possibili applicazioni di questo metodo allo studio delle proprietà di analiticità.
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The research reported in this document has been supported in part by the Aerospace Research Laboratories, OAR, under Grant AF-EOAR-64-20, through the European Office of Aerospace Research, United States Air Force.
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Peres, A. On Schwinger’s Parametrization of Feynman Graphs. Nuovo Cim 38, 270–284 (1965). https://doi.org/10.1007/BF02750455
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DOI: https://doi.org/10.1007/BF02750455