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The mass eigenvalue problem in aSU 2-invariant pseudoscalar meson theory with an indefinite metric

Проблема собственных эначений массы вSU 2-инвариантной псевдоскалярной меэонной теории с индефинитной метрикой

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Il Nuovo Cimento A (1965-1970)

Summary

We regularize the conventionalSU 2-invariant pseudoscalar meson theory by introducing an indefinite-metric space. All quantities entering our model are finite. This fact enables us to state a mass eigenvalue problem for the π-N system in a way free from the usual troubles due to the appearance of divergences. Moreover, a relation between the renormalized coupling constantG R and the ratio of the pion mass to the nucleon one is obtained.

Riassunto

Si regolarizza la teoria mesonica pseudoscalare convenzionale invariante rispetto aSU 2 introducendo uno spazio a metrica indefinita. Tutte le grandezze che figurano nel modello sono finite. Questo fatto permette di formulare un problema agli autovalori per le masse, per il sistema π-N, in un modo privo di complicazioni dovute a divergenze. Si deduce inoltre una relazione tra la costante di accoppiamento rinormalizzataG R ed il rapporto tra la massa pionica e quella nucleonica.

Реэюме

Мы регуляриэуем обшепринятуюSU 2-инвариантную псевдоскалярную меэонную теорию эа счет введения пространства с индефинитной метрикой. Все величины, входяшие в нащу модель, являются конечными. Этот факт поэволяет нам сформулировать проблему собственных эначений массы для π-N системы, в некотором смысле, свободную от обычных осложнений, свяэанных с появлением расходимостей. Кроме того, получается сотнощение между перенормированной константой свяэиG R и отнощением массы пиона к массе нуклона.

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References

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Authors and Affiliations

  1. Istituto di Scienze Fisiche dell’Università, Milano

    C. Marioni & E. Montaldi

  2. Sezione di Milano, Istituto Nazionale di Fisica Nucleare, Italy

    E. Montaldi

Authors
  1. C. Marioni
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  2. E. Montaldi
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Marioni, C., Montaldi, E. The mass eigenvalue problem in aSU 2-invariant pseudoscalar meson theory with an indefinite metric. Nuov Cim A 12, 997–1015 (1972). https://doi.org/10.1007/BF02747862

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  • DOI: https://doi.org/10.1007/BF02747862

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