"Classical field theory and classical mechanics"의 두 판 사이의 차이

2010년 3월 16일 (화) 09:32 판

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

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

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

@@ 12번째 줄: / 12번째 줄: @@
 <h5>Euler-Lagrange equation</h5>
-* if field satisfies the equation of motion, EL is satisfied
+*  if field satisfies the equation of motion, EL is satisfied<br><math>\partial_\mu \left( \frac{\partial \mathcal{L}}{\partial ( \partial_\mu \psi )} \right) - \frac{\partial \mathcal{L}}{\partial \psi} = 0.</math><br>
@@ 20번째 줄: / 20번째 줄: @@
 <h5>equation of continuity</h5>
-*  current density <math>J_{\mu}</math> satisfies<br><math>\partial^{\mu} J_{\mu}=0</math><br>
+*  current density <math>J_{\mu}=(J_0,J_1,J_2,J_3)</math> satisfies<br><math>\partial^{\mu} J_{\mu}=0</math><br>
-*  we get a 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
+<h5>currents</h5>
+* quantum analogues of the conser
@@ 60번째 줄: / 70번째 줄: @@
 * 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