# Symmetry in EM

### Discrete symmetry

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

What happens under spacetime inversion?

### Dual transformation

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

 $\mathbf{E}\rightarrow c\mathbf{B}$ $\mathbf{B}\rightarrow -\mathbf{E}/c$