skip to content
Emmy Noether's wonderful theorem Preview this item
ClosePreview this item
Checking...

Emmy Noether's wonderful theorem

Author: Dwight E Neuenschwander
Publisher: Baltimore, Md. : Johns Hopkins University Press, ©2011.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"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
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Named Person: Emmy Noether; Emmy Noether
Document Type: Book
All Authors / Contributors: Dwight E Neuenschwander
ISBN: 0801896940 9780801896941 9780801896934 0801896932
OCLC Number: 654748881
Description: xviii, 243 pages : illustrations ; 22 cm
Contents: 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.
Responsibility: Dwight E. Neuenschwander.
More information:

Abstract:

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

Reviews

Editorial reviews

Publisher Synopsis

Neuenschwander writes well and gives thorough explanations. Choice 2011

 
User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.

Similar Items

Related Subjects:(5)

User lists with this item (1)

Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/654748881> # Emmy Noether's wonderful theorem
    a schema:CreativeWork, schema:Book ;
    library:oclcnum "654748881" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/mdu> ;
    library:placeOfPublication <http://experiment.worldcat.org/entity/work/data/568994197#Place/baltimore_md> ; # Baltimore, Md.
    schema:about <http://id.worldcat.org/fast/1744696> ; # Noether's theorem
    schema:about <http://dewey.info/class/539.725/e22/> ;
    schema:about <http://experiment.worldcat.org/entity/work/data/568994197#Topic/invariantentheorie> ; # Invariantentheorie
    schema:about <http://experiment.worldcat.org/entity/work/data/568994197#Topic/noether_theorem> ; # Noether-Theorem
    schema:about <http://experiment.worldcat.org/entity/work/data/568994197#Person/noether_emmy_1882_1935> ; # Emmy Noether
    schema:about <http://viaf.org/viaf/73918294> ; # Emmy Noether
    schema:author <http://viaf.org/viaf/39275008> ; # Dwight E. Neuenschwander
    schema:bookFormat bgn:PrintBook ;
    schema:copyrightYear "2011" ;
    schema:datePublished "2011" ;
    schema:description ""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 angular momentum, respectively. This exciting result offers a rich unifying principle for all of physics."@en ;
    schema:description ""Dwight E. Neuenschwander's introduction to the theorem's genesis, applications, and consequences artfully unpacks its universal importance and unsurpassed elegance. Drawing from over thirty years of teaching the subject, Neuenschwander uses mechanics, optics, geometry, and field theory to point the way to a deep understanding of Noether's Theorem. The three sections provide a step-by-step, simple approach to the less-complex concepts surrounding the theorem, in turn instilling the knowledge and confidence needed to grasp the full wonder it encompasses. Illustrations and worked examples throughout each chapter serve as signposts on the way to this apex of physics."--Publisher's description."@en ;
    schema:description "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."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/568994197> ;
    schema:inLanguage "en" ;
    schema:name "Emmy Noether's wonderful theorem"@en ;
    schema:productID "654748881" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/654748881#PublicationEvent/baltimore_md_johns_hopkins_university_press_2011> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/568994197#Agent/johns_hopkins_university_press> ; # Johns Hopkins University Press
    schema:workExample <http://worldcat.org/isbn/9780801896934> ;
    schema:workExample <http://worldcat.org/isbn/9780801896941> ;
    umbel:isLike <http://bnb.data.bl.uk/id/resource/GBB0A4537> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/654748881> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/568994197#Agent/johns_hopkins_university_press> # Johns Hopkins University Press
    a bgn:Agent ;
    schema:name "Johns Hopkins University Press" ;
    .

<http://experiment.worldcat.org/entity/work/data/568994197#Person/noether_emmy_1882_1935> # Emmy Noether
    a schema:Person ;
    schema:birthDate "1882" ;
    schema:deathDate "1935" ;
    schema:familyName "Noether" ;
    schema:givenName "Emmy" ;
    schema:name "Emmy Noether" ;
    .

<http://experiment.worldcat.org/entity/work/data/568994197#Place/baltimore_md> # Baltimore, Md.
    a schema:Place ;
    schema:name "Baltimore, Md." ;
    .

<http://experiment.worldcat.org/entity/work/data/568994197#Topic/invariantentheorie> # Invariantentheorie
    a schema:Intangible ;
    schema:name "Invariantentheorie"@en ;
    .

<http://id.worldcat.org/fast/1744696> # Noether's theorem
    a schema:Intangible ;
    schema:name "Noether's theorem"@en ;
    .

<http://viaf.org/viaf/39275008> # Dwight E. Neuenschwander
    a schema:Person ;
    schema:familyName "Neuenschwander" ;
    schema:givenName "Dwight E." ;
    schema:name "Dwight E. Neuenschwander" ;
    .

<http://viaf.org/viaf/73918294> # Emmy Noether
    a schema:Person ;
    schema:birthDate "1882" ;
    schema:deathDate "1935" ;
    schema:familyName "Noether" ;
    schema:givenName "Emmy" ;
    schema:name "Emmy Noether" ;
    .

<http://worldcat.org/isbn/9780801896934>
    a schema:ProductModel ;
    schema:isbn "0801896932" ;
    schema:isbn "9780801896934" ;
    .

<http://worldcat.org/isbn/9780801896941>
    a schema:ProductModel ;
    schema:isbn "0801896940" ;
    schema:isbn "9780801896941" ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.