2
The equations of motion for a classical field $\phi$ can be obtained using the Lagrange: $$ \frac{\partial \mathcal{L}}{\partial \phi} - \partial_\mu \bigg ( \frac{\partial \mathcal{L}}{\partial(\partial_\mu \phi)} \bigg )=0 \tag{1}$$ A simple Lagrangian: $$ \mathcal{L} = \frac{1}{2} \partial_\mu...