"Symmetry and conserved quantitiy : Noether's theorem"의 두 판 사이의 차이

2012년 10월 28일 (일) 17:55 판

\(\alpha_{s}\) continuous symmetry with parameter s
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
\(Q(t)=\int_V J_0(x) \,d^3 x\)
\(\frac{dQ}{dt}=0\)

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 * [http://en.wikipedia.org/wiki/Noether%27s_theorem http://en.wikipedia.org/wiki/Noether's_theorem]
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