Geometric Formulation of Higher-Order Lagrangian Systems in Supermechanics

摘要

Using supervector fields along a morphism of graded manifolds, we study both the geometry of the tangent supermanifolds of an arbitrary order and kth-order ordinary differential superequations, in order to develop the higher-order Lagrangian formalism of supermechanics. In particular, we obtain, in this formalism, a generalization of Noether's theorem and its converse.