"연속 방정식"의 두 판 사이의 차이

2012년 6월 11일 (월) 02:17 판

current \(j(x)=(j_0(x),j_1(x),j_2(x),j_3(x))\) 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

current
\(j(x)=(j^0(x),j^1(x),j^2(x),j^3(x))\)
\(j^{\mu}(x)= \frac{\partial \mathcal{L}}{\partial ( \partial_\mu \phi )}\left(\frac{\partial\alpha_{s}(\phi)}{\partial s} \right) \)

obeys the continuity equation
\(\partial_{\mu} J^{\mu}=\sum_{\mu=0}^{3}\frac{\partial j^{\mu}}{\partial x^{\mu}}=0\)
\(j^{4}(x)\) density of some abstract fluid
\(\mathbf{J}=(j_x,j_y,j_z)\) velocity of this abstract fluid at each space time point
conserved charge
\(Q(t)=\int_V J_0(x) \,d^3 x\)
\(\frac{dQ}{dt}=0\)

@@ 8번째 줄: / 8번째 줄: @@
+<h5>notation</h5>
+* f
+*  current <math>j(x)=(j_0(x),j_1(x),j_2(x),j_3(x))</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>
+* Lagrangian can be used to express the current density explicity
+*  current <br><math>j(x)=(j^0(x),j^1(x),j^2(x),j^3(x))</math><br><math>j^{\mu}(x)= \frac{\partial \mathcal{L}}{\partial ( \partial_\mu \phi )}\left(\frac{\partial\alpha_{s}(\phi)}{\partial s} \right) </math><br>
+*  obeys the continuity equation<br><math>\partial_{\mu} J^{\mu}=\sum_{\mu=0}^{3}\frac{\partial j^{\mu}}{\partial x^{\mu}}=0</math><br>
+* <math>j^{4}(x)</math> density of some abstract fluid
+* <math>\mathbf{J}=(j_x,j_y,j_z)</math> velocity of this abstract fluid at each space time point
+*  conserved charge<br><math>Q(t)=\int_V J_0(x) \,d^3 x</math><br><math>\frac{dQ}{dt}=0</math><br>  <br>
@@ 51번째 줄: / 72번째 줄: @@
 <h5>관련된 항목들</h5>
+* [[맥스웰 방정식]]