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

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.

3 pages