Noether conservation laws issue from the gauge invariance of an Euler-Lagrange operator, but not a Lagrangian

TL;DR

The paper demonstrates that gauge invariance of an Euler-Lagrange operator, rather than the Lagrangian itself, can lead to Noether conservation laws, highlighting a nuanced aspect of gauge theories.

Contribution

It reveals that gauge invariance of the Euler-Lagrange operator alone can produce Noether conservation laws, independent of the Lagrangian's gauge invariance.

Findings

Gauge invariance of Euler-Lagrange operators can generate conservation laws.

Lagrangians with the same Euler-Lagrange operator may differ in gauge invariance.

Conservation laws can arise from gauge invariance at the operator level, not just the Lagrangian level.

Abstract

As is well known, there are different Lagrangians which lead to the same Euler-Lagrange operator. The gauge invariance of a Lagrangian guarantees that of the corresponding Euler-Lagrange operator, but not vice versa. We show that the gauge invariance of an Euler-Lagrange operator, but not a Lagrangian results in Noether conservation laws.