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$F^\alpha_\gamma$ is the usual EM stress tensor $F^{\alpha\gamma}$ with the $\gamma$ index lowered. This is accomplished using the following identity: $$F^\alpha_\gamma=g_{\gamma\mu}F^{\alpha\mu}$$ where $g$ is the metric tensor.


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If the change in magnetic field can be neglected, it is called electrostatics. In this case, you can define an electric potential $V$: $$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} = 0 \Rightarrow \mathbf{E} = - \nabla V$$ If the change in the electric field and electric current can be neglected, it is called magnetostatics. In this ...


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Let $Q(\Omega)$ denote the charge inside the volume $\Omega\subset\mathbb R^3$. We have $$ Q(\Omega)=\int_\Omega\rho(\vec x)\,\mathrm d\vec x\tag1 $$ where $\vec x\in\mathbb R^3$. If you change variables $\vec x\to-\vec x$ you get $$ Q(\Omega)=\int_{\Omega'}\rho(-\vec x)\,\mathrm d\vec x\tag2 $$ where $\Omega'$ is the image of $\Omega$ under $\vec x\to-\vec ...


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I believe you are confused as to what a parity transformation actually is. Parity transformations are changes of coordinate system, in which we simply modify how we label points in space. Let's say you write down a coordinate system in which some point $p$ has coordinates $(x,y,z)=(1,0,1)$, and let the charge density there be $\rho$. Now, you decide that ...


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