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The Noether theorems: invariance and conservation laws in the twentieth century

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Bibliographische Detailangaben
Beteilige Person:	Kosmann-Schwarzbach, Yvette 1941- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York, NY [u.a.] Springer 2011
Schriftenreihe:	Sources and Studies in the History of Mathematics and Physical Series
Schlagwörter:	Noether, Emmy > 1882-1935 Noether-Theorem
Links:	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
Umfang:	XIII, 205 S. Ill.
ISBN:	9780387878676

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Datensatz im Suchindex

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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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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
work_keys_str_mv	AT kosmannschwarzbachyvette lestheoremesdenoether AT kosmannschwarzbachyvette thenoethertheoremsinvarianceandconservationlawsinthetwentiethcentury

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