The Lorentz-Abraham-Dirac (LAD) equation for a free particle (without any external force) is \begin{equation} m \frac{d u^{\mu}}{d\tau} = \frac{\mu_{0} e^2}{6 \pi c}\left[ \frac{d^2 u^{\mu}}{d\tau^2} - u^{\mu} \left( \frac{d u_{\nu}}{d\tau} \frac{d u^{\nu}}{d\tau} \right) \right]. \end{equation} I know that this equation have runaway solutions and other issues. I just want to know if there's a Lagrangian that give back this equation? I guess there is none.
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