"Symmetry and conserved quantitiy : Noether's theorem"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
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| − | + | ==introduction</h5> | |
* fields | * fields | ||
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| − | + | ==field theoretic formulation</h5> | |
* <math>\alpha_{s}</math> continuous symmetry with parameter s | * <math>\alpha_{s}</math> continuous symmetry with parameter s | ||
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| − | + | ==history</h5> | |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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| − | + | ==related items</h5> | |
* [[correlation functions and Ward identity]] | * [[correlation functions and Ward identity]] | ||
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| − | + | ==books</h5> | |
* [[Emmy Noether’s Wonderful Theorem]] | * [[Emmy Noether’s Wonderful Theorem]] | ||
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| − | + | ==expositions</h5> | |
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| − | + | ==question and answers(Math Overflow)</h5> | |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
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| − | + | ==blogs</h5> | |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
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| − | + | ==experts on the field</h5> | |
* http://arxiv.org/ | * http://arxiv.org/ | ||
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| − | + | ==links</h5> | |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | * [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내] | ||
2012년 10월 28일 (일) 14:02 판
==introduction
- fields
- the condition for the extreme of a functional leads to Euler-Lagrange equation
- invariance of functional imposes another constraint
- Noether's theorem : extreme+invariance -> conservation law
==field theoretic formulation
- \(\alpha_{s}\) continuous symmetry with parameter s
- current
\(j(x)=(j^0(x),j^1(x),j^2(x),j^3(x))\)
\(j^{\mu}(x)= \frac{\partial \mathcal{L}}{\partial ( \partial_\mu \phi )}\left(\frac{\partial\alpha_{s}(\phi)}{\partial s} \right) \)
- obeys the continuity equation
\(\partial_{\mu} J^{\mu}=\sum_{\mu=0}^{3}\frac{\partial j^{\mu}}{\partial x^{\mu}}=0\) - \(j^{4}(x)\) density of some abstract fluid
- \(\mathbf{J}=(j_x,j_y,j_z)\) velocity of this abstract fluid at each space time point
- conserved charge
\(Q(t)=\int_V J_0(x) \,d^3 x\)
\(\frac{dQ}{dt}=0\)
==history
==related items
encyclopedia
- http://en.wikipedia.org/wiki/Noether's_theorem
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
==books
- Emmy Noether’s Wonderful Theorem
- 2011년 books and articles
- http://library.nu/search?q=
- http://library.nu/search?q=
==expositions
articles
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
==question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/search?q=
- http://physics.stackexchange.com/search?q=
==blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
==experts on the field
==links