Discussion on the equivalence of two relativistic point-particle Lagrangians

Liubin Wang, Xin Wu

In 2021, Lei et al. claimed the equivalence between the two Lagrangians ${\mathcal{L}}_1=-mc\sqrt{-g_{\mu \nu }{\dot{x}}^{\mu }{\dot{x}}^{\nu }}-V$ and $\mathcal{L}_2 = \frac{1}{2}mg_{μν} {\dot{x}}…