Local invariance and covariant conservation laws are independent in field theories; the paper gives requirements for Noether's second theorem to produce the latter and shows the two are not equivalent.
On the conservation laws of electrodynamics
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Covariant conservation laws, local invariance and Noether's second theorem
Local invariance and covariant conservation laws are independent in field theories; the paper gives requirements for Noether's second theorem to produce the latter and shows the two are not equivalent.