Il Nuovo Cimento B (1971-1996)

, Volume 34, Issue 2, pp 334–344 | Cite as

An operator approach to symmetries

  • F. Magri
Article
First Online:
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Summary

By using the methods of nonlinear functional analysis a single general operator symmetry condition is derived. It supplies a simple and systematic procedure for finding symmetry conditions in particular problems. From it the Lie algebra structure associated with symmetries is easily displayed and the classical Lie theory of symmetries of differential equations is obtained without needing the technique of the group extension.

Операторный подход к симметриям

Резюме

Используя методы нелинейного функционального анализа, выводится условие симметрии отдельного общего оператора. Предлагается простая и систематическая процедура нахождения условий симметрии в конкретных проблемах. С помощью предложенного метода легко проявляется структура алгебры Ли, связанная с симметриями, и получается классическая теория Ли симметрий дифференциальных уравнений, без использования техники расширения групп.

Riassunto

Facendo uso dei metodi dell'analisi funzionale non lineare si deduce un'unica e generale condizione di simmetria in forma operatoriale. La sua applicazione fornisce un procedimento semplice e sistematico per trovare le condizioni di simmetria in problemi particolari. Ad esempio essa permette di sviluppare la teoria delle simmetrie delle equazioni differenziali senza dover far uso della tecnica dei gruppi estesi di Lie. Tale condizione, inoltre, può essere assunta come punto di partenza per una sistematica indagine delle conseguenze delle proprietà di simmetria. In questo lavoro essa viene utilizzata per mettere in luce la struttura di algebra di Lie associata alle simmetrie di un qualunque tipo di equazione.

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Copyright information

© Società Italiana di Fisica 1976

Authors and Affiliations

  • F. Magri
    • 1
  1. 1.Istituto di Matematica del PolitecnicoMilanoItalia

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