Classical field theory and classical mechanics

introduction

• can be formulated using classical fields and lagrangian density
• change the coordinates and fields accordingly
• require the invariance of action integral over arbitrary region
• this invariance consists of two parts : Euler-Lagrange equation and the equation of continuity

 

 

Euler-Lagrange equation

• if field satisfies the equation of motion, EL is satisfied
  \(\partial_\mu \left( \frac{\partial \mathcal{L}}{\partial ( \partial_\mu \psi )} \right) - \frac{\partial \mathcal{L}}{\partial \psi} = 0.\)
  

 

 

equation of continuity

• current density \(J_{\mu}=(J_0,J_1,J_2,J_3)\) satisfies
  \(\partial^{\mu} J_{\mu}=0\)
  
• we get a conserved quantity
  \(G=\int_V J_0(x) \,d^3 x\)
  
• Lagrangian can be used to express the current density explicity

 

 

 

currents

• quantum analogues of the conser

 

 

history

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

 

 

related items

• Electromagnetism

 

 

books

 

• 찾아볼 수학책
  
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://gigapedia.info/1/
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

encyclopedia

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/Classical_field_theory
• http://en.wikipedia.org/wiki/Continuity_equation
• http://en.wikipedia.org/wiki/current_density
• http://en.wikipedia.org/wiki/Noether's_theorem
• http://en.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• Princeton companion to mathematics(Companion_to_Mathematics.pdf)

 

 

question and answers(Math Overflow)

• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=
• http://mathoverflow.net/search?q=

 

 

blogs

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=
  • http://blogsearch.google.com/blogsearch?q=

 

 

articles

 

• 논문정리
• http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
• http://www.ams.org/mathscinet
• http://www.zentralblatt-math.org/zmath/en/
• http://pythagoras0.springnote.com/
• http://math.berkeley.edu/~reb/papers/index.html
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
• http://dx.doi.org/

 

 

experts on the field

• http://arxiv.org/