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Emmy Noether's wonderful theorem

Autor Dwight E Neuenschwander
Vydavatel: Baltimore, Md. : Johns Hopkins University Press, ©2011.
Vydání/formát:   book_printbook : EnglishZobrazit všechny vydání a formáty
Databáze:WorldCat
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"A beautiful piece of mathematics, Noether's Theorem touches on every aspect of physics. Emmy Noether proved her theorem in 1915 and published it in 1918. This profound concept demonstrates the connection between conservation laws and symmetries. For instance, the theorem shows that a system invariant under translations of time, space, or rotation will obey the laws of conservation of energy, linear momentum, or
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Osoba: Emmy Noether; Emmy Noether
Typ dokumentu: Book
Všichni autoři/tvůrci: Dwight E Neuenschwander
ISBN: 0801896940 9780801896941 9780801896934 0801896932
OCLC číslo: 654748881
Popis: xviii, 243 pages : illustrations ; 22 cm
Obsahy: Preface --
Acknowledgments --
Glossary of symbols --
Primary and auxiliary questions --
1 PROLOGUE --
1.1 Symmetry, invariance, and conservation laws --
1.2 Emmy Noether biographical notes --
WHEN FUNCTIONALS ARE EXTREMAL --
2 Functionals --
2.1 Single-integral functionals --
2.2 Formal definition of a functional --
3 Extremals --
3.1 The Euler-Lagrange Equation --
3.2 Corollaries to the Euler-Lagrange Equation --
3.3 On the equivalence of Hamilton's Principle and Newton's Second Law --
3.4 Where did Hamilton's Principle come from? --
3.5 Why kinetic minus potential energy? --
3.6 Extremals with external constraints --
When functionals are invariant --
4 Invariance --
4.1 Formal definition of Invariance --
4.2 Condition for Invariance: The Rund-Trautman Identity --
4.3 A more liberal definition of Invariance --
5 Emmy Noether's Elegant Theorem --
5.1 Extremal + Invariance = Noether's Theorem --
5.2 The inverse problem: Finding invariances --
5.3 Adiabatic Invariance and Noether's Theorem --
THE INVARIANCE OF FIELDS --
6 Fields and Noether's theorem --
6.1 Multiple-integral functionals --
6.2 Euler-Lagrange Equations for Fields --
6.3 Canonical momenta and the Hamiltonian for Fields --
6.4 Equations of Continuity --
6.5 The Rund-Trautman Identity for Fields --
6.6 Noether's Theorem for Fields --
6.7 Complex fields --
6.8 Global Gauge transformations --
7 Gauge Invariance as a dynamical principle --
7.1 Local Gauge Invariance and the covariant derivative --
7.2 Electrodynamics as a Gauge Theory I: Field tensors --
7.3 Pure electrodynamics, spacetime invariances, and conservation laws --
7.4 Electrodynamics as a Gauge Theory II: Sources and minimal coupling --
7.5 Internal degrees of freedom --
7.6 Non-Abelian Gauge transformations --
POST-NOETHER INVARIANCE --
8 Invariance in phase space --
8.1 Phase Space --
8.2 Hamilton's Principle in Phase Space --
8.3 Noether's Theorem through Hamilton's Equations --
8.4 Hamilton-Jacobi Theory --
9 The action as a generator --
9.1 Conservation of probability and unitary transformations --
9.2 Continuous spacetime transformations in quantum mechanics --
9.3 Epilogue --
APPENDIXES --
A. Scalars, vectors, tensors, and coordinate transformations --
B. Special relativity --
C. Equations of motion in quantum mechanics --
D. Legendre transformations and conjugate variables --
E. The Jacobian --
Bibliography --
Index.
Odpovědnost: Dwight E. Neuenschwander.
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