The Noether theorems: invariance and conservation laws in the twentieth century
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2011
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| Schriftenreihe: | Sources and Studies in the History of Mathematics and Physical Series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 205 S. Ill. |
| ISBN: | 9780387878676 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804142700811780096 |
|---|---|
| adam_text | Titel: The Noether theorems
Autor: Kosmann-Schwarzbach, Yvette
Jahr: 2011
Contents
Preface............................................................ vii
Acknowledgments.................................................. ix
Part I Invariant Variational Problems by Emmy Noether.
Translation of Invariante Variationsprobleme (1918)
Invariant Variational Problems...................................... 3
1 Preliminary Remarks and the Formulation ofthe Theorems....... 3
2 Divergence Relations and Identities........................... 7
3 Converse in the Case of a Finite Group......................... 10
4 Converse in the Case of an Infinite Group...................... 12
5 Invariance ofthe Various Elements ofthe Relations.............. 16
6 An Assertion of Hubert ..................................... 19
Part II Invariance and Conservation Laws in the Twentieth Century.
The Inception and Reception ofthe Noether Theorems
Introduction....................................................... 25
1 The Inception ofthe Noether Theorems........................... 29
1.1 From the Theory of Invariants to Special Relativity.............. 29
1.2 The General Theory of Relativity and the Problem of the
Conservation of Energy..................................... 37
1.3 The Publications of Hubert and Klein on General Relativity....... 39
1.4 Emmy Noether at Göttingen................................. 43
1.5 After Göttingen............................................ 53
2 The Noether Theorems ......................................... 55
2.1 Preliminaries.............................................. 56
2.2 The First Theorem: Conservation Laws........................ 57
2.3 The Second Theorem: Differential Identities.................... 60
2.4 Conclusion: The DiscussionofHilbert s Assertion............... 63
xii Contents
3 The Noether Theorems as Seen by Contemporaries and by
Historians of Science........................................... 65
3.1 References to Noether in the Works of Klein, Hubert and Weyl,
and in Einstein s Correspondence............................. 65
3.2 The Eulogies of 1935....................................... 76
3.3 Personal Recollections...................................... 79
3.4 The Introduction to Noether s Gesammelte Abhandlungen /
Collected Papers........................................... 86
3.5 Translations ofthe Invariante Variationsprobleme............... 87
3.6 Historical Analyses......................................... 88
4 The Transmission of Noether s Ideas, from Bessel-Hagen
to Hill, 1921-1951.............................................. 91
4.1 Bessel-Hagen and Symmetries up to Divergence................. 91
4.2 Pauli 1921 and 1941........................................ 93
4.3 Weitzenböck 1923.......................................... 94
4.4 Courant and Hubert 1924.................................... 95
4.5 In Quantum Mechanics...................................... 96
4.6 Negative Results........................................... 98
4.7 Hill s 1951 Article.......................................... 101
5 The Reception of Noether s First Theorem after 1950..............103
5.1 Symmetries and Conservation Laws in Classical Mechanics and
Quantum Physics...........................................104
5.2 On Some Encyclopedia Articles..............................104
5.3 Analysis of Several Works in Mathematics and Mechanics,
1950-1980................................................105
5.4 Analysis of Several Works in Physics, 1950-1980...............117
5.5 The Rediscoveries as Generalizations of Noether s Theorem .....121
6 The Reception of Noether s Second Theorem after 1950............123
6.1 The Second Theorem and General Relativity....................123
6.2 The Second Theorem and Gauge Theories......................129
7 After 1970?Genuine Generalizations............................133
7.1 Jet Bundles and Generalized Symmetries.......................134
7.2 Characteristics of Conservation Laws and the Converse
ofthe First Theorem........................................137
7.3 The Formal Calculus of Variations............................138
7.4 Symmetries and Conservation Laws for Nonvariational Equations .. 140
7.5 At the end ofthe twentieth Century............................144
Conclusion ........................................................145
Appendix I. Postcard from Noether to Klein, 15 February 1918..........149
Appendix II. Letter from Noether to Klein, 12 March 1918..............153
Contents xiii
Apppendix III. Letter from Klein to Pauli, 8 March 1921 ...............159
Apppendix IV. Letter from Noether to Einstein, 7 January 1926.........161
Apppendix V. Lectures at the Mathematical Society of Göttingen,
1915-1919.....................................................167
References.........................................................171
Index.............................................................199
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| isbn | 9780387878676 |
| language | English |
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| series2 | Sources and Studies in the History of Mathematics and Physical Series |
| spelling | Kosmann-Schwarzbach, Yvette 1941- Verfasser (DE-588)14349645X aut Les théorèmes de Noether The Noether theorems invariance and conservation laws in the twentieth century Yvette Kosmann-Schwarzbach New York, NY [u.a.] Springer 2011 XIII, 205 S. Ill. txt rdacontent n rdamedia nc rdacarrier Sources and Studies in the History of Mathematics and Physical Series Noether, Emmy 1882-1935 (DE-588)118588443 gnd rswk-swf Noether-Theorem (DE-588)4401301-2 gnd rswk-swf Noether-Theorem (DE-588)4401301-2 s Noether, Emmy 1882-1935 (DE-588)118588443 p 1\p DE-604 Erscheint auch als Online-Ausgabe 978-0-387-87868-3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020132150&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kosmann-Schwarzbach, Yvette 1941- The Noether theorems invariance and conservation laws in the twentieth century Noether, Emmy 1882-1935 (DE-588)118588443 gnd Noether-Theorem (DE-588)4401301-2 gnd |
| subject_GND | (DE-588)118588443 (DE-588)4401301-2 |
| title | The Noether theorems invariance and conservation laws in the twentieth century |
| title_alt | Les théorèmes de Noether |
| title_auth | The Noether theorems invariance and conservation laws in the twentieth century |
| title_exact_search | The Noether theorems invariance and conservation laws in the twentieth century |
| title_full | The Noether theorems invariance and conservation laws in the twentieth century Yvette Kosmann-Schwarzbach |
| title_fullStr | The Noether theorems invariance and conservation laws in the twentieth century Yvette Kosmann-Schwarzbach |
| title_full_unstemmed | The Noether theorems invariance and conservation laws in the twentieth century Yvette Kosmann-Schwarzbach |
| title_short | The Noether theorems |
| title_sort | the noether theorems invariance and conservation laws in the twentieth century |
| title_sub | invariance and conservation laws in the twentieth century |
| topic | Noether, Emmy 1882-1935 (DE-588)118588443 gnd Noether-Theorem (DE-588)4401301-2 gnd |
| topic_facet | Noether, Emmy 1882-1935 Noether-Theorem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020132150&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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