
The action of a field $\phi^\mu$ in flat $n$-dimensional spacetime is
$$ S = \int \text{d}^n x \mathscr{L}(\phi^\mu(x),\partial_\alpha \phi^\mu(x)) $$
From an infinitesimal variation of field configuration, and discarding a boundary term, we have E-L equations
$$ \frac{\partial \mathscr{L}}{\part...