In mathematics, Noether identities characterize the degeneracy of a Lagrangian system.
A Lagrangian L is called degenerate if the Euler–Lagrange operator of L satisfies non-trivial Noether identities.
Higher-stage Noether identities also are separated into trivial and non-trivial cases.
A degenerate Lagrangian is called reducible if there exist non-trivial higher-stage Noether identities.
Formulated in a very general setting, second Noether’s theorem associates to the Koszul–Tate complex of reducible Noether identities, parameterized by antifields, the BRST complex of reducible gauge symmetries parameterized by ghosts.