= Time reversal of an electromagnetic gauge field
{title2=$A_0(x)\mapsto A_0(x_T),\quad A_i(x)\mapsto-A_i(x_T)$}
The vector <Dirac current> has an even temporal component and odd spatial components under <time-reversal symmetry>. Invariance of its real minimal coupling therefore gives the displayed transformation of the <gauge field>, up to a <gauge transformation>. Differentiation at $x_T=(-x^0,\boldsymbol x)$ yields $F_{\mu\nu}(x)\mapsto-t_\mu t_\nu F_{\mu\nu}(x_T)$, with $t=(1,-1,-1,-1)$. Thus the <electric field> is even and the <magnetic field> is odd.
Back to article page
