Symmetry in EM

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Discrete symmetry

Space inversion ([math]\mathbf{r} \rightarrow -\mathbf{r}[/math]) Time inversion ([math]t \rightarrow -t[/math])
[math]\rho \rightarrow \rho[/math] [math]\rho \rightarrow \rho[/math]
[math]\mathbf{j} \rightarrow -\mathbf{j}[/math] [math]\mathbf{j} \rightarrow -\mathbf{j}[/math]
[math]\mathbf{v} \rightarrow -\mathbf{v}[/math] [math]\mathbf{v} \rightarrow -\mathbf{v}[/math]
[math]\mathbf{F} \rightarrow -\mathbf{F}[/math] [math]\mathbf{F} \rightarrow \mathbf{F}[/math]
[math]\mathbf{E} \rightarrow -\mathbf{E}[/math] [math]\mathbf{E} \rightarrow \mathbf{E}[/math]
[math]\mathbf{B} \rightarrow \mathbf{B}[/math] [math]\mathbf{B} \rightarrow -\mathbf{B}[/math]
[math]V \rightarrow V[/math] [math]V \rightarrow V[/math]
[math]\mathbf{A} \rightarrow -\mathbf{A}[/math] [math]\mathbf{A} \rightarrow -\mathbf{A}[/math]

What happens under spacetime inversion?

Dual transformation

In source-free case, Maxwell's equations are invariant under dual transformation:

[math]\mathbf{E}\rightarrow c\mathbf{B}[/math] [math]\mathbf{B}\rightarrow -\mathbf{E}/c[/math]