"Classical field theory and classical mechanics"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
| 4번째 줄: | 4번째 줄: | ||
* change the coordinates and fields accordingly | * change the coordinates and fields accordingly | ||
* require the invariance of action integral over arbitrary region | * require the invariance of action integral over arbitrary region | ||
| + | * this invariance consists of two parts : Euler-Lagrange equation and the equation of continuity | ||
| 20번째 줄: | 21번째 줄: | ||
* current density <math>J_{\mu}</math> satisfies<br><math>\partial^{\mu} J_{\mu}=0</math><br> | * current density <math>J_{\mu}</math> satisfies<br><math>\partial^{\mu} J_{\mu}=0</math><br> | ||
| − | * conserved quantity<br><math>G:=\int_V J_0(x) \,d^3 x</math><br> | + | * we get a conserved quantity<br><math>G:=\int_V J_0(x) \,d^3 x</math><br> |
| + | * Lagrangian can be used to express the current density explicity | ||
| + | |||
| + | |||
2010년 3월 3일 (수) 18:44 판
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
equation of continuity
- current density \(J_{\mu}\) 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
history
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/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
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