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Metric structures and chiral symmetries

Метрические структуры и чиральные симметрим

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Il Nuovo Cimento A (1965-1970)

Summary

Various aspects of nonlinear-group realizations are discussed and it is shown that the nonlinearSU 3×SU 3 chiral-invariant meson Lagrangian, and hence the meson-meson low-energy processes, can be expressed completely in terms of the canonical metric on the group space ofSU 3.

Riassunto

Si discutono vari aspetti delle realizzazioni di gruppo non lineari, e si dimostra che si può esprimere compiutamente in termini della metrica canonica nello spazio del gruppoSU 3 la lagrangiana del mesone non lineare chiralmente invariante inSU 3×SU 3, e quindi i processi a bassa energia mesone-mesone.

Резюме

Обсуждаются различные аспектя нелинейных грунновых представлений, и показывается, что нелинейныйSU 3×SU 3 чираляный инвариантный мезонный Пагранжиан и, следовательно, мезон-мезонные процессы при малых энерчиях мочут быть полностью выражены в терминах канонической метрики в групповом пространствеSU 3.

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Literatur

  1. J. Schwinger:Phys. Lett.,24 B, 9 (1967).

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  2. J. Wess andB. Zumino:Lagrangian method for chiral symmetries, New York University preprint, June 1967.

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  5. This point is discussed in ref. (4).S. Coleman, C. G. Callan, J. Wess andB. Zumino:The structure of phenomenological Lagrangians, I, II, New York University preprint.

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  7. The relevant differential geometry may be found in:S. Helgason Differential Geometry and Symmetric Spaces (New York, 1962);S. Kobayashi andK. Nomizu:Foundations of Differential Geometry (New York, 1963);R. Bishop andR. Crittenden:Geometry of Manifolds (New York, 1964).

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  10. See the Appendix and alsoK. Yano:The Theory of Lie Derivatives and Its Applications (Amsterdam, 1955).

  11. C. Isham andA. Patani:Meson-meson scattering lengths from chiral SU 3×SU3 ICTP/68/1 preprint, to appear inNuovo Cimento

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Authors and Affiliations

  1. Physics Department, Imperial College, London

    C. J. Isham

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  1. C. J. Isham
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Additional information

The research reported in this document has been sponsored in part by the Air Force Office of Scientific Research OAR through the European Office of Aerospace Research, United States Air Force.

Traduzione a cura della Redazione.

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Isham, C.J. Metric structures and chiral symmetries. Nuovo Cimento A (1965-1970) 61, 188–202 (1969). https://doi.org/10.1007/BF02755123

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  • DOI: https://doi.org/10.1007/BF02755123

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