On the inversion of Noether's theorem in the Lagrangian formalism: II.—Classical field theory

• Autor(a) principal: Candotti, E.
• Data de Publicação: 1970
• Outros Autores: Palmieri, C., Vitale, B.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1007/BF02758981; http://hdl.handle.net/11449/231135

Both the «direct» and the «inverse» Noether's theorems are generalized to allow for infinitesimal transformations that add to the action functional an integral over a 4-divergence and an integral over a function vanishing «on the orbit» (Noether transformations). It is then shown that: i) to every Noether transformation there corresponds a «weak» continuity equation and a family of Nother transformations (Noether family) defining the same continuity equation; ii) every Noether family contains an invariance transformation; iii) to every «weak» continuity equation there corresponds a Noether family; iv) every Noether family contains a subset of Noether transformations equivalent to a 4-divergence translation of the Lagrangian density. © 1970, Società Italiana di Fisica. All rights reserved.