dorsal/arxiv
View SchemaInvariant Variation Problems
| Authors | Emmy Noether, M. A. Tavel |
|---|---|
| Categories | |
| ArXiv ID | physics/0503066 |
| URL | https://arxiv.org/abs/physics/0503066 |
| DOI | 10.1080/00411457108231446 |
| Journal | Gott.Nachr.1918:235-257,1918; Transp.Theory Statist.Phys.1:186-207,1971 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
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.
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"abstract": "The problems in variation here concerned are such as to admit a continuous\ngroup (in Lie\u0027s sense); the conclusions that emerge from the corresponding\ndifferential equations find their most general expression in the theorems\nformulated in Section 1 and proved in following sections. Concerning these\ndifferential equations that arise from problems of variation, far more precise\nstatements can be made than about arbitrary differential equations admitting of\na group, which are the subject of Lie\u0027s researches. What is to follow,\ntherefore, represents a combination of the methods of the formal calculus of\nvariations with those of Lie\u0027s group theory. For special groups and problems in\nvariation, this combination of methods is not new; I may cite Hamel and\nHerglotz for special finite groups, Lorentz and his pupils (for instance\nFokker), Weyl and Klein for special infinite groups. Especially Klein\u0027s second\nNote and the present developments have been mutually influenced by each other,\nin which regard I may refer to the concluding remarks of Klein\u0027s Note.",
"arxiv_id": "physics/0503066",
"authors": [
"Emmy Noether",
"M. A. Tavel"
],
"categories": [
"physics.hist-ph"
],
"doi": "10.1080/00411457108231446",
"journal_ref": "Gott.Nachr.1918:235-257,1918; Transp.Theory\n Statist.Phys.1:186-207,1971",
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Invariant Variation Problems",
"url": "https://arxiv.org/abs/physics/0503066"
},
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