If you set up $S = \int dt ( \dot{x}^{\mu} p_{\mu} - \frac{e}{2}p^{\mu}p_{\mu} - \frac{i}{2} \chi_{\mu} \dot{\chi}^{\mu} - \frac{ik}{2} \psi \chi^{\mu} p_{\mu})$ and eliminate the momentum via it's eom to get $p_{\mu} = e^{-1}(\dot{x}_{\mu} - \frac{ik}{2}\psi \chi_{\mu})$ and plug it in to that action, you're supposed to get $S = \int d t \frac{1}{2}(e^{-1}\dot{x}^{\mu} \dot{x}^{\nu} - i \chi^{\mu} \dot{\chi}^{\nu} - i k e^{-1} \psi \dot{x}^{\mu} \dot{\chi}^{\nu}) \eta_{\mu \nu}$
but I keep getting extra terms: