High Quality Content by WIKIPEDIA articles! In mathematics, Noether identities characterize the degeneracy of a Lagrangian system. Given a Lagrangian system and its Lagrangian L, Noether identities can be defined as a differential operator whose kernel contains a range of the Euler–Lagrange operator of L. Any Euler–Lagrange operator obeys Noether identities which therefore are separated into the trivial and non-trivial ones. A Lagrangian L is called degenerate if the Euler–Lagrange operator of L satisfies non-trivial Noether identities. In this case Euler–Lagrange equations are not independent.

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