| 拉格朗日量 | 运动方程 |
| 经典力学 | \(\mathcal{L}=\frac{1}{2}mv^2-V\) | \(F=ma\) |
| 电动力学 | \(\mathcal{L}=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-J_{\mu}A^{\mu}\) | \(\partial^{\mu}F_{\mu\nu}=J_{\nu}\) |
| 狭义相对论 | \(\mathcal{L}=-\gamma mc^2=1/\sqrt{1-v^2/c^2}\) | \(p=\gamma mv\) |
| 广义相对论 | \(\mathcal{L}=(\alpha R-2\alpha\Gamma+\mathcal{L}_m\)\sqrt{-g}\) | \(R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R+\Lambda g_{\mu\nu}=\frac{8\pi G}{c^4}T_{\mu\nu}\) |
| 量子力学 | \(\mathcal{L}=p\dot{q}-\hat{H}(p,q)\) | \(i\hbar\frac{\partial \psi}{\partial t}=\hat{H}\psi\) |
| Yang-Mills场 | \(\mathcal{L}=-\frac{1}{4}F^{\alpha\mu\nu}F_{\mu\nu}^{\alpha}\) | \(\mathcal{D}_{\mu}F^{\mu\nu}=0\) |