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Some remarks on the Bethe-Salpeter normalization properties

  • E. Predazzi
Article

Summary

The Bethe-Salpeter normalization condition is investigated and a unified picture of the different methods so far used is given together with their equivalence proof. The solutions of the Bethe-Salpeter equation are then examined in the Wick-Cutkosky model forn=l+1 for a check of the recent result of Nakanishi that abnormal solutions with oddx correspond to states with negative norm. This result is confirmed forn=l+1 and arbitraryx in the energy range 0<sn/(n+x)n+x+1) for which it is proved that the solution can be well approximated by the zero energy solution.

Keywords

Negative Norm Unify Picture Explicit Normalization Fuchsian Singularity Solid Harmonic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Riassunto

Si studia la condizione di normalizzazione dell'equazione di Bethe-Salpeter ed un quadro completo dei diversi metodi usati finora viene presentato insieme con la dimostrazione che tutti questi metodi sono equivalenti. Le soluzioni dell'equazione di Bethe-Salpeter sono considerate nell'ambito del modello di Wick-Cutkosky pern=l+1 allo scopo di verificare il risultato recentemente ottenuto da Nakanishi che le soluzioni anormali conx dispari corrispondono a stati di norma negativa. Questo risultato è provato perx qualsiasi nel dominio di energiesn/(n+x)n+x+1) per il quale si dimostra che la soluzione è ben approssimata dalla soluzione corrispondente ad energia nulla.

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Copyright information

© Società Italiana di Fisica 1965

Authors and Affiliations

  • E. Predazzi
    • 1
  1. 1.The Enrico Fermi Institute for Nuclear StudiesThe University of ChicagoChicago

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