Summary
It is shown that a Feynman amplitude has singularities on the physical boundary if and only if the relevant Feynman diagram can be interpreted as a picture of an energy- and momentum-conserving process occurring in space-time, with all internal particles real, on the mass shell, and moving forward in time. As a by-product of the proof, the Feynman parameter associated with an internal line is identified (within a proportionality factor) with the time the particle exists between collisions, divided by its mass.
Riassunto
Si mostra che un’ampiezza di Feynman ha singolarità al contorno fisico, se, e solo se, il relativo diagramma di Feynman puÒ essere interpretato come la descrizione di un processo di conservazione nello spazio-tempo dell’energia e dell’impulso, cou tutte le particelle interne reali sullo strato della massa, e dotate di moto in avanti nel tempo. Come risultato accessorio di questa dimostrazione, il parametra di Feynman associato ad una linea interna si identifica (a meno di un fattore di proporzionalità) con il tempo in cui la particella esiste fra le collisioni, diviso per la massa della particella.
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Coleman, S., Norton, R.E. Singularities in the physical region. Nuovo Cim 38, 438–442 (1965). https://doi.org/10.1007/BF02750472
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DOI: https://doi.org/10.1007/BF02750472