"Electromagnetics"의 두 판 사이의 차이

2013년 3월 23일 (토) 10:15 판

the electromagnetic potential is a connection on a U(1)-bundle on spacetime whose curvature is the electromagnetic field
the electromagnetism is a gauge field theory with structure group U(1)

almost all forces in mechanics are conservative forces, those that are functions only of positions, and certainly not functions of velocities
Lorentz force is a rare example of velocity dependent force

total energy of a charge particle in an electromagnetic field
\(E=\frac{1}{2m}(p_j-eA_{j})(p_j-eA_j)+q\phi\)
replace the momentum with the canonical momentum
- similar to covariant derivative

http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Quigley.pdf
Feynman's proof of Maxwell equations and Yang's unification of electromagnetic and gravitational Aharonov–Bohm effects

@@ 29번째 줄: / 29번째 줄: @@
 ==Lagrangian formulation==
+* [[Lagrangian formulation of electromagetism]]
-*  Lagrangian for a charged particle in an electromagnetic field <math>L=T-V</math>
-:<math>L(q,\dot{q})=m||\dot{q}||-e\phi+eA_{i}\dot{q}^{i}</math><br>
-*  action
-:<math>S=-\frac{1}{4}\int F^{\alpha\beta}F_{\alpha\beta}\,d^{4}x</math><br>
-*  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<br><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.<br>
-* force on a particle is same as <math>e\mathbf{E}+e\mathbf{v}\times \mathbf{B}</math>
-* THOMAS YU [http://math.uchicago.edu/~may/REU2012/REUPapers/Yu.pdf LAGRANGIAN FORMULATION OF THE ELECTROMAGNETIC FIELD]
-* http://dexterstory.tistory.com/888<br>
-* [[path integral formulation of quantum mechanics|path integral]]<br>
@@ 105번째 줄: / 88번째 줄: @@
 ==books==
+* ELECTROMAGNETIC THEORY AND COMPUTATION
-ELECTROMAGNETIC THEORY AND COMPUTATION
 [[분류:math and physics]]