Let’s consider electromagnetic Lagrangian
$$\mathcal L=-{1\over 4}F_{\mu\nu}F^{\mu\nu}\tag{1}$$
Is charge conservation derived as a consequence of $U(1)$-invariance of this Lagrangian?
Let’s consider electromagnetic Lagrangian
$$\mathcal L=-{1\over 4}F_{\mu\nu}F^{\mu\nu}\tag{1}$$
Is charge conservation derived as a consequence of $U(1)$-invariance of this Lagrangian?