Symmetry and conserved quantitiy : Noether's theorem

introduction

• \(\alpha_{s}\) 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

• http://www.google.com/search?hl=en&tbs=tl:1&q=

 

 

related items

• correlation functions and Ward identity

 

 

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=

 

 

 

 

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://blogsearch.google.com/blogsearch?q=
    
  • http://blogsearch.google.com/blogsearch?q=
• http://ncatlab.org/nlab/show/HomePage

 

 

experts on the field

• http://arxiv.org/

 

 

links

• Detexify2 - LaTeX symbol classifier
• 수식표현 안내