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Il Nuovo Cimento (1955-1965)

, Volume 2, Issue 1, pp 120–134 | Cite as

Propagators of quantized field

  • P. T. Matthews
  • A. Salam
Article

Summary

Feynman’s formulation of quantum mechanics—the sum over histories—is discussed in its field theoretic form. It expresses the propagators of the interacting fields as functional integrals over the fields. The integrals over the anti-commuting Fermi fields are carried out. The complete propagators, including all radiative corrections, are thus expressed as functional integrals, over the meson field, of integrands involving the single nucleon propagator and the vacuum to vacuum transition amplitude in an external field. The latter factor is the Fredholm determinant of the external field problem for « nucleons » satisfying Fermi statistics, but its inverse if Bose statistics are assumed. These expressions for the propagators display some interesting distinctions between « renormalizable » and « unrenormalizable » interactions which are quite independent of an expansion in the coupling constant.

Riassunto

Si discute l’estensione alla teoria dei campi della formulazione di Feynman della meccanica quantistica — la somma rispetto alle « storie ». Si sviluppano gli integrali sui campi di Fermi anticommutativi. I propagatori completi, comprese tutte le correzioni radiative, si esprimono così come integrali funzionali sul campo mesonico di integrandi comprendenti il propagatore del nucleone isolato e l’ampiezza di transizione vuoto-vuoto in un campo esterno. Quest’ultimo fattore è il determinante di Fredholm del problema del campo esterno per «nucleone » che soddisfano la statistica di Fermi, ma è il suo inverso se le particelle obbediscono alla statistica di Bose. Queste espressioni pei propagatori mettono in risalto alcune interessanti distinzioni tra interazioni « rinormalizzabili » e « non rinormalizzabili » del tutto indipendenti dallo sviluppo in serie della costante di accoppiamento.

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Copyright information

© Società Italiana di Fisica 1955

Authors and Affiliations

  • P. T. Matthews
    • 1
  • A. Salam
    • 2
  1. 1.Department of Mathematical PhysicsThe UniversityBirminghamEngland
  2. 2.St. John’s CollegeCambridgeEngland

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