= Geometrization of the Lorentz force by an affine connection
{title2=$\Gamma^i{}_{tt}=-E^i,\quad\Gamma^i{}_{tj}=\epsilon^i{}_{jk}B^k$}
For smooth stationary fields on $\mathbb R^3$, set $\Gamma^i{}_{tt}=-E^i$ and $\Gamma^i{}_{tj}=\Gamma^i{}_{jt}=\epsilon^i{}_{jk}B^k$, with all other <Christoffel symbols> zero. This <torsion-free connection> makes the equation $\ddot{\mathbf x}=\mathbf E+2\mathbf B\times\dot{\mathbf x}$ a <geodesic equation> with time as <affine parameter>. Arbitrary smooth fields suffice; a metric realization imposes additional potential conditions.
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