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Emmy Noether's wonderful theorem

著者: Dwight E Neuenschwander
出版商: Baltimore, Md. : Johns Hopkins University Press, ©2011.
版本/格式:   Print book : 英语查看所有的版本和格式
数据库:WorldCat
提要:
"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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提及的人: Emmy Noether; Emmy Noether
文件类型:
所有的著者/提供者: Dwight E Neuenschwander
ISBN: 0801896940 9780801896941 9780801896934 0801896932
OCLC号码: 654748881
描述: xviii, 243 pages : illustrations ; 22 cm
内容: 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.
责任: Dwight E. Neuenschwander.
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摘要:

This handy guide includes end-of-chapter questions for review and appendixes detailing key related physics concepts for further study.  再读一些...

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Neuenschwander writes well and gives thorough explanations. Choice 2011

 
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