I am studying Coulomb and Lorentz gauge. Lorentz gauge help produce wave equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\nabla^2 V-\mu_0\epsilon_0\frac{\partial^2V}{\partial t^2}=-\frac{\rho}{\epsilon_0},\;and\;\nabla^2 \vec A-\mu_0\epsilon_0\frac{\partial^2\vec A}{\partial t^2}=-\mu_0\vec J[/tex]

Where the 4 dimensional d'Alembertian operator:

[tex]\square^2=\nabla^2-\mu_0\epsilon_0\frac{\partial^2}{\partial t^2}[/tex]

[tex]\Rightarrow\;\square^2V=-\frac{\rho}{\epsilon_0},\; and\;\square^2\vec A=-\mu_0\vec J[/tex]

So the wave equations are really 4 dimensional d'Alembertian equations?

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# D'Alembertian and wave equation.

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