"Classical field theory and classical mechanics"의 두 판 사이의 차이
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| 108번째 줄: | 108번째 줄: | ||
* [[Electromagnetics|Electromagnetism]] | * [[Electromagnetics|Electromagnetism]] | ||
| − | * [[Einstein field equation]] | + | * [[Einstein field equation|Einstein field hequation]] |
* [[symplectic geometry|sympletic geometry]] | * [[symplectic geometry|sympletic geometry]] | ||
* [[5 integrable systems and solvable models|integrable Hamiltonian systems and solvable models]] | * [[5 integrable systems and solvable models|integrable Hamiltonian systems and solvable models]] | ||
| 142번째 줄: | 142번째 줄: | ||
* Classical mechanics [[2610572/attachments/1142452|Classical_Mechanics.djvu]]V.I. Arnold<br> | * Classical mechanics [[2610572/attachments/1142452|Classical_Mechanics.djvu]]V.I. Arnold<br> | ||
| + | * Electrodynamics and Classical Theory of Fields and Particles http://library.nu/docs/1U9OCRM7QY/Electrodynamics and Classical Theory of Fields and Particle<br> | ||
* [[2010년 books and articles]]<br> | * [[2010년 books and articles]]<br> | ||
2011년 10월 1일 (토) 07:22 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
- three important conserved quantity
- energy
- momentum
- angular momentum
notation
- \(T\) kinetic energy
- \(V\) potential energy
- We have Lagrangian \(L=T-V\)
- Define the Hamiltonian
- \(H =p\dot q-L\)
- \(p\dot q\) is twice of kinetic energy
- Thus the Hamiltonian represents \(H=T+V\) the total energy of the system
Lagrangian formalism
Hamiltonian mechanics
- conjugate variables are on the equal footing
- 고전역학에서의 가적분성 항목 참조
Poisson bracket
For \(f(p_i,q_i,t), g(p_i,q_i,t)\) , we define the Poisson bracket
\(\{f,g\} = \sum_{i=1}^{N} \left[ \frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} - \frac{\partial f}{\partial p_{i}} \frac{\partial g}{\partial q_{i}} \right]\)
In quantization we have correspondence
\(\{f,g\} = \frac{1}{i}[u,v]\)
phase space
canonically conjugate momentum
links and webpages
question and answers(Math Overflow)
history
- Electromagnetism
- Einstein field hequation
- sympletic geometry
- integrable Hamiltonian systems and solvable models
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://ko.wikipedia.org /wiki/작용
- http://en.wikipedia.org/wiki/Canonical_coordinates
- http://en.wikipedia.org/wiki/Lagrangian_mechanics
- http://en.wikipedia.org/wiki/Lagrangian
- http://en.wikipedia.org/wiki/poisson_bracket
- http://en.wikipedia.org/wiki/Action_(physics)
- http://en.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- Classical mechanics Classical_Mechanics.djvuV.I. Arnold
- Electrodynamics and Classical Theory of Fields and Particles http://library.nu/docs/1U9OCRM7QY/Electrodynamics and Classical Theory of Fields and Particle
articles
- 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/
blogs
experts on the field