"Lagrangian formulation of electromagetism"의 두 판 사이의 차이

2020년 11월 13일 (금) 10:43 기준 최신판

@@ 1번째 줄: / 1번째 줄: @@
-==Lagrangian for a particle==
+* {{수학노트|url=전자기학의_라그랑지안}}
-*  Lagrangian for a charged particle in an electromagnetic field <math>L=T-V</math>
+* [[path integral formulation of quantum mechanics]]
-:<math>L(q,\dot{q})=m||\dot{q}||-e\phi+eA_{i}\dot{q}^{i}</math>
+* [[Electroweak theory]]
-*  action
+[[분류:migrate]]
-:<math>S=-\frac{1}{4}\int F^{\alpha\beta}F_{\alpha\beta}\,d^{4}x</math>
-*  Euler-Lagrange equations
-:<math>p_{i}=\frac{\partial{L}}{\partial{\dot{q}^{i}}}=m\frac{\dot{q}_{i}}{||\dot{q}_{i}||}+eA_{i}=mv_{i}+eA_{i}</math>
-$$
-F_{i}=\frac{\partial{L}}{\partial{q^{i}}}=\frac{\partial}{\partial{{q}^{i}}}(eA_{j}\dot{q}^{j})=e\frac{\partial{A_{j}}}{\partial{q}^{i}}\dot{q}^{j}
-$$
-*  equation of motion<math>\dot{p}=F</math> Therefore we get
-:<math>m\frac{dv_{i}}{dt}=eF_{ij}\dot{q}^{j}</math>. This is what we call the Lorentz force law.
-* force on a particle is same as <math>e\mathbf{E}+e\mathbf{v}\times \mathbf{B}</math>
-==Lagrangian for electromagnetic tensor==
-* 상호작용이 없는 전자기장의 라그랑지안은 다음과 같다
-$$\mathcal{L}_{\text{EM}}= - \frac{1}{4}F_{\mu\nu}F^{\mu\nu}=\frac{1}{2}(\mathbf{E}^2-\mathbf{B}^2)$$
-이 때 <math>F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu \,\!</math>는 전자기텐서, $A=(A_{\mu})$는 전자기 포텐셜
-* 라그랑지안은 전자기 포텐셜의 다음과 같은 변환에 대하여 불변이다
-:<math>A_{\mu}(x) \to A_{\mu}(x)-\partial_{\mu}\Lambda(x)</math>
-여기서 $\Lambda(x)$는 임의의 스칼라장
-* equation of motion
-$$
-= \partial_\mu F^{\mu\nu}
-$$
-* see http://www.damtp.cam.ac.uk/user/tong/qft/six.pdf
-==memo==
-* http://dexterstory.tistory.com/888
-==related items==
-* [[path integral formulation of quantum mechanics|path integral]]
-==expositions==
-* THOMAS YU [http://math.uchicago.edu/~may/REU2012/REUPapers/Yu.pdf LAGRANGIAN FORMULATION OF THE ELECTROMAGNETIC FIELD]
-* [http://www.physics.sfsu.edu/~lea/courses/grad/fldlagr.PDF The field Lagrangian]
-* http://www.lecture-notes.co.uk/susskind/classical-mechanics/lecture-8/the-electromagnetic-lagrangian/
-* http://unapologetic.wordpress.com/2012/07/16/the-higgs-mechanism-part-1-lagrangians/
-==questions==
-* http://physics.stackexchange.com/questions/3005/derivation-of-maxwells-equations-from-field-tensor-lagrangian?rq=1

"Lagrangian formulation of electromagetism"의 두 판 사이의 차이

2020년 11월 13일 (금) 10:43 기준 최신판

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