Abstract
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.
How to cite this document
Candotti, E.; Palmieri, C.; Vitale, B.. On the inversion of Noether's theorem in the Lagrangian formalism: II.—Classical field theory. Il Nuovo Cimento A, v. 70, n. 2, p. 233-246, 1970. Available at: <
http://hdl.handle.net/11449/231135>.