Summary
The usual geometric interpretation of the theory of the gauge fields is implemented and generalized, utilizing concepts of the metrical Riemannian geometry. A classic theorem—due to Riemann and Vermeil—allows us to give an elementary solution to the problem of the passage from the field strength (curvature) to the potential (connection).
Riassunto
Utilizzando concetti della geometria riemanniana, si dà un'interpretazione geometrica della teoria dei campi digauge, che è al contempo piú «microscopica» e piú generale di quella usuale. Un classico teorema di Riemann e Vermeil consente di risolvere su un piano elementare il problema del passaggio dall'intensità di campo (curvatura) al potenziale (connessione).
Резюме
Используя концепции метрической римановой геометрии, развивается и обобщается обычная геометрическая интерпретация теории калибровочных полей. Классическая теорема, предложенная Риманом и Вермейлом, позволяет получить элементарное решение проблемы перехода от интенсивности поля (кривизны) к потенциалу (связи).
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References
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Loinger, A. Metrical geometry of the classical gauge fields. Nuov Cim A 86, 259–271 (1985). https://doi.org/10.1007/BF02902551
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DOI: https://doi.org/10.1007/BF02902551