.

0 (hodnocen0 x )

BK

New York : Springer, c2011

xiii, 205 s. : il. ; 24 cm

ISBN 978-0-387-87867-6 (váz.)

Sources and studies in the history of mathematics and physical series

francouzština

Přeloženo z francouzštiny?

Obsahuje bibliografické odkazy a rejstřík

000195586

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 of the 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 of the Various Elements of the Relations... 16 // 6 An Assertion of Hilbert ... 19 // Part II Invariance and Conservation Laws in the Twentieth Century. // The Inception and Reception of the Noether Theorems // Introduction... 25 // 1 The Inception of the 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 Hilbert 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 Discussion of Hilbert’s Assertion... 63 // xi // 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. Hilbert 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 of the 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 Hilbert 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 // of the 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 of the 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