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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?

Qmechanic
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Kutasov
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  • Possible duplicates: https://physics.stackexchange.com/q/2721/2451 and links therein. – Qmechanic Mar 10 '24 at 08:51
  • I vote to reopen because the question is specifically about gauge invariance as an explanation of charge conservation. – my2cts Mar 10 '24 at 09:10
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    My answer:

    Charge conservation is related to the invariance of the Lagrangian under rotation in the complex plane, or, equivalently, under a complex phase shift, such as $$\phi \rightarrow \phi + i\delta \phi ~.$$

    Often it is considered a consequence of electromagnetic gauge invariance. However, charge is also conserved in the absence of electromagnetism. It is therefore better to say that gauge invariant electromagnetism can only describe conserved charge.

     – my2cts Mar 10 '24 at 09:13

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