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Alternative Lagrangians and complete integrability: Some remarks

Альтернативные Лагранжианы и полная интегрирыемость

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

The properties of a (1–1) tensor field, derived from two alternative Lagrangians, are studied, with respect to the problem of complete integrability. Out of the initial pair of alternative Lagrangians we get an infinite set of alternative Lagrangians if the (1–1) tensor field satisfies the Nijenhuis condition. Some examples are given.

Riassunto

Si studiano le proprietà di un campo tensoriale (1–1), costruito a partire da due lagrangiane equivalenti, in connessione con il problema della completa integrabilità. A partire dalla coppia iniziale di lagrangiane alternative se ne costruiscono infinite se il campo tensoriale (1–1) soddisfa la condizione di Njienhuis. Si considerano alcuni esempi.

Резюме

Исследуются свойства (1–1)-тензорного поля, сконструированного из двух альтернативных Лагранжианов, в связи с проблемой полной интегрируемости. Исходя из пары альтернативных Лагранжианов, мы получаем бесконечную систему альтернативных Лагранжианов, если (1–1)-тензорное поле удовлетворяет условию Нейнхэйса. Приводятся некоторые примеры.

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Author notes

  1. P. Antonini, G. Marmo & C. Rubano

    Present address: Mostra d’Oltremare, pad. 19, 80125, Napoli, Italia

Authors and Affiliations

  1. Scuola di Perfezionamento in Fisica Teorica e Nucleare dell’Università degli Studi, Napoli, Italia

    P. Antonini

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Italia

    G. Marmo

  3. Istituto di Fisica Teorica dell’Università, Napoli, Italia

    G. Marmo & C. Rubano

Authors
  1. P. Antonini
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  2. G. Marmo
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  3. C. Rubano
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Antonini, P., Marmo, G. & Rubano, C. Alternative Lagrangians and complete integrability: Some remarks. Nuov Cim B 86, 17–30 (1985). https://doi.org/10.1007/BF02732269

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  • DOI: https://doi.org/10.1007/BF02732269

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