On the low Lagrangian formulation of Vlasov-Poisson equations

Abstract

In this work, two problems related with the Low Lagrangian formulation of the Vlasov-Poisson equations are solved. The first problem is related to the space on which the Low Lagrangian is defined. It is shown that the Low Lagrangian is defined on the tangent bundle of the densities of configuration space. The second problem is related to the assumptions which are called Low constraints. It is shown that Low constraints amount to the fact that the Low Lagrangian is invariant under a group action.