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Il Nuovo Cimento (1955-1965)

, Volume 16, Issue 3, pp 560–568 | Cite as

On the renormalization of the axial vector coupling constant in β-decay

  • J. Bernstein
  • M. Gell-Mann
  • L. Michel
Article

Summary

The models of the axial vector current discussed byGell-Mann andLévy are examined further. Generalized Ward identities are derived for the axial vector weak vertex. It is then shown that in theσ model and the non-linear model the renormalization factor —GA/G may be expressed as a matrix element in the theory of strong interactions. Thus in theσ model, which is renormalizable, —GA/G is finite in every order. Since —GA/G exhibits divergences in the non-linear model, that model is not renormalizable in the usual sense.

Riassunto

Si esaminano ulteriormente i modelli della corrente vettoriale assiale discussi daFeynman, Gell-Mann eLévy. Si derivano identità generalizzate di Ward per il vertice debole del vettore assiale. Si mostra poi che nel modelloσ e nel modello non lineare il fattore di rinormalizzazione —GA/G può essere espresso come un elemento di matrice nella teoria delle interazioni forti. Così nel modelloσ, che è rinormalizzabile, —GA/G è finito in ogni ordine. Poichè —GA/G presenta divergenze nel modello non lineare, questo modello non è rinormalizzabile nel senso usuale.

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References

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Copyright information

© Società Italiana di Fisica 1960

Authors and Affiliations

  • J. Bernstein
    • 1
  • M. Gell-Mann
    • 2
  • L. Michel
    • 3
    • 4
  1. 1.Faculté des SciencesOrsay (S. et O.)
  2. 2.Collège de France and Ecole Normale SupérieureParis
  3. 3.Faculté des SciencesOrsay (S. et O.)
  4. 4.Service de Physique Théorique, Groupe IIOrsay (S. et O.)

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