Summary
A consideration of the integral equation for the vertex function derived from field theory leads to a proof of a new form of Levinson’s theorem. The number of CDD poles, which occur at first-sheet zeros of the vertex function, must be supplemented by the number of second-sheet zeros of the vertex function, at which points occur the poles of the amplitude associated with particles for which the wave-function renormalization constant vanishes.
Riassunto
Lo studio dell’equazione integrale per la funzione di vertice dedotta dalla teoria dei campi porta alla dimostrazione di una nuova forma del teorema di Levinson. Al numero di poli CDD, che stanno negli zeri del primo foglietto della funzione di vertice, deve essere aggiunto il numero degli zeri del secondo foglietto della funzione di vertice, nei quali punti si trovano i poli dell’ampiezza associata a particelle per le quali la costante di rinormalizzazione della funzione d’onda tende a zero.
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The research reported in this document has been sponsored in part by the Air Force Office of Scientific Eesearch OAE through the European Office Aerospace United States Air Force.
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Charap, J.M. A field-theoretic proof of a modified version of Levinson’s theorem. Nuovo Cim 36, 419–435 (1965). https://doi.org/10.1007/BF02751320
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DOI: https://doi.org/10.1007/BF02751320