Symmetries in Lagrangian Field Theory

Abstract

By generalizing the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first order jet bundles $J^1\pi$ of a fiber bundle $\pi :E\to {\mathbb{R}}^k$ where ${\mathbb{R}}^k$ is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether Theorem is proved.

26 pages, pre-published version in Reports on Mathematical Physics, 2015

References in corpus (2)

• On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
• Symmetries, Newtonoids vector fields and conservation laws in the Lagrangian $k$-symplectic formalism

Cited by in corpus (3)

• On k-polycosymplectic Marsden-Weinstein reductions
• Geometry of Classical Nambu-Goldstone Fields
• An energy-momentum method for ordinary differential equations with an underlying $k$-polysymplectic manifold