Noether's Second Theorem

Noether's Second Theorem is a result of mathematics and theoretical physics, proved by Emmy Noether alongside her more widely known first theorem, relating the symmetries of an action functional that depend on arbitrary functions of position, rather than on constant parameters, to a system of differential identities among the equations of motion. It governs the local, or gauge, symmetries found in field theories such as general relativity and electromagnetism, in contrast to the global symmetries and conserved quantities covered by Noether's first theorem.