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

Noether theorem for mu-symmetries / G. Cicogna, G. Gaeta. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 40:39(2007), pp. 11899-11921.

Noether theorem for mu-symmetries

G. Gaeta
Ultimo
2007

Abstract

We give a version of Noether theorem adapted to the framework of μ-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of λ-symmetries, and connects μ-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this ‘μ-conservation law’ actually reduces to a standard one; we also note a relation between μ-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under μ-prolonged variation fields, leading to modified Euler–Lagrange equations. In this setting, μ-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.
Settore MAT/07 - Fisica Matematica
2007
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/36426
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