Noether theorem for mu-symmetries

Details Noether theorem for mu-symmetries Noether theorem for mu-symmetries

2007-08-23

arxiv.org/abs/0708.3144v1

Physics

Mathematical Physics

28 pages, to appear in J. Phys. A

Scientific paper

10.1088/1751-8113/40/39/013

We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this "mu-conservation law'' actually reduces to a standard one; we also note a relation between mu-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under mu-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting mu-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.

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