Summary
Underlying gauge symmetries of integrable field theories can be used to find the infinitestimal version of Bäcklund transformations whose global extension exhausts all the solutions of the corresponding nonlinear equations. We discuss the Liouville equation in which the conserved currents are obtained without using the action principle and that makes it possible to find its connection with self-dual guage theories.
Riassunto
Le simmetrie di gauge sottostanti alle teorie di campo integrabili si possono usare per trovare la versione infinitesimale delle trasformazioni di Bäcklund la cui estensione globale esaurisce tutte le soluzioni delle corrispondenti equazioni non lineari. Si discute l’equazione di Liouville in cui le correnti conservate si ottengono senza usare il principio di azione e che rende possibile trovare la sua connessione con le teorie di gauge autoduali.
Резюме
Калибровочные симметрии интегрируемых полевых теорий могут быть использованы для нахождения бесконечно малых преобразований Бэклунда, глобальное расширение которых исчерцывает все решения соответствующих нелинейных уравнений. Мы обсуждаем уравнение Лиувилля, где сохраняющиеся токи получаются без использования принципа действия и что позволяет получить связь с дуальными калибровочными теориями.
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Bhattacharya, G., Bohr, H. Symmetries and conserved currents from infinitesimal Bäcklund transformations. Nuov Cim A 80, 393–400 (1984). https://doi.org/10.1007/BF02773502
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DOI: https://doi.org/10.1007/BF02773502