The Noether Theorems

Abstract

This chapter will deal briefly with the results stated and proved by Noether in the Invariante Variationsprobleme1 [1918c]. Her originality in this article consisted in dealing with problems that arose either in classical mechanics (the first theorem) or in general relativity (the second theorem). We emphasize what has been ignored by most authors who have cited this article, that in it Noether treated a problem of very great generality, since she dealt with a Lagrangian of arbitrary order with an arbitrary number of independent variables,2 as well as an arbitrary number of dependent variables, and considered the invariance of such Lagrangians under the action of groups of infinitesimal transformations.