Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory

Details Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory

2007-03-12

arxiv.org/abs/math-ph/0703035v1

Rev.Math.Phys.19:1117-1147,2007

Physics

Mathematical Physics

29 pages

Scientific paper

10.1142/S0129055X07003188

This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.

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