Invariant variation problems
Abstract
The problems in variation here concerned are such as to admit a continuous group (in Lie's sense); the conclusions that emerge from the corresponding differential equations find their most general expression in the theorems formulated in Section 1 and proved in following sections. Concerning these differential equations that arise from problems of variation, far more precise statements can be made than about arbitrary differential equations admitting of a group, which are the subject of Lie's researches. What is to follow, therefore, represents a combination of the methods of the formal calculus of variations with those of Lie's group theory. For special groups and problems in variation, this combination of methods is not new; I may cite Hamel and Herglotz for special finite groups, Lorentz and his pupils (for instance Fokker), Weyl and Klein for special infinite groups. Especially Klein's second Note and the present developments have been mutually influenced by each other, in which regard I may refer to the concluding remarks of Klein's Note.
 Publication:

Transport Theory and Statistical Physics
 Pub Date:
 January 1971
 DOI:
 10.1080/00411457108231446
 arXiv:
 arXiv:physics/0503066
 Bibcode:
 1971TTSP....1..186N
 Keywords:

 Physics  History and Philosophy of Physics
 EPrint:
 M. A. Tavel's English translation of Noether's Theorems (1918), reproduced by Frank Y. Wang. Thanks to Lloyd Kannenberg for corrigenda