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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Lorenz gauge condition ： ウィキペディア英語版 Lorenz gauge condition In electromagnetism, the Lorenz gauge or Lorenz gauge condition is a partial gauge fixing of the electromagnetic vector potential. The condition is that $\backslash partial\_\backslash mu\; A^\backslash mu=0$. This does not completely fix the gauge: one can still make a gauge transformation $A^\backslash mu\backslash to\; A^\backslash mu+\backslash partial^\backslash mu\; f$ where $f$ is a harmonic scalar function (that is, a scalar function satisfying $\backslash partial^\backslash mu\backslash partial\_\backslash mu\; f=0$, the equation of a massless scalar field). The Lorenz condition is used to eliminate the redundant spin-0 component in the (1/2,1/2) representation of the Lorentz group. It is equally used for massive spin-1 fields where the concept of gauge transformations does not apply at all. The Lorenz condition is named after Ludvig Lorenz. It is a Lorentz invariant condition, and is frequently called the "Lorentz condition" because of confusion with Hendrik Lorentz, after whom Lorentz covariance is named. ==Description== In electromagnetism, the Lorenz condition is generally used in calculations of time-dependent electromagnetic fields through retarded potentials.〔 and (【引用サイトリンク】url=http://www.physics.princeton.edu/~mcdonald/examples/jefimenko.pdf ).〕 The condition is :$\backslash partial\_A^\backslash mu\; \backslash equiv\; A^\backslash mu\}\; +\; \backslash frac\backslash frac=0.$ where $\backslash vec$ is the magnetic vector potential and $\backslash ,\backslash varphi$ is the electric potential; see also Gauge fixing. In Gaussian units the condition is: :$\backslash nabla\backslash cdot\backslash frac=0.$ A quick justification of the Lorenz gauge can be found using Maxwell's equations and the relation between the magnetic vector potential and the magnetic field: :$\backslash nabla\backslash times\backslash vec=-\backslash frac=\backslash nabla\backslash times-\backslash frac$ Therefore, :$\backslash nabla\backslash times(\backslash vec+\backslash frac)=0$ Since the curl is zero, that means there is a scalar function $\backslash ,\backslash varphi$ such that $-\backslash nabla\backslash ,\backslash varphi=\backslash vec+\backslash frac$. This gives the well known equation for the electric field, $\backslash vec=-\backslash nabla\backslash ,\backslash varphi-\backslash frac$. This result can be plugged into another one of Maxwell's equations, :$)\}=\}=\backslash frac\}=\backslash nabla\backslash frac-\backslash frac\backslash frac\}$ This leaves, :$\backslash nabla(\backslash nabla\backslash cdot\backslash vec+\backslash frac\backslash frac)=\backslash mu\_0\backslash vec-\backslash frac\backslash frac+\backslash nabla^2\backslash vec$ To have Lorentz invariance, the time derivatives and spatial derivatives must be treated equally (i.e. of the same order). Therefore it is convenient to choose the Lorenz gauge condition, which gives the result : These are simpler and more symmetric forms of the inhomogeneous Maxwell's equations. Note that the Coulomb gauge also fixes the problem of Lorentz invariance, but leaves a coupling term with first-order derivatives. Here $c=\backslash frac$ and $\backslash vec\; B=\backslash nabla\backslash times\; \backslash vec\; A\backslash ,.$ The explicit solutions for $\backslash ,\backslash varphi$ and $\backslash vec\; A$ – unique, if all quantities vanish sufficiently fast at infinity – are known as retarded potentials. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lorenz gauge condition」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.