Variational principles on <i>r</i>th order jets of fibre bundles in field theory

Abstract

The Hamilton and the modified Hamilton variational principles in classical field theory are studied for physical systems described by Lagrangian and Hamiltonian densities depending on arbitrary order derivatives of the field. These principles are established on the fibre bundles Jr(E), J1(Jr−1(E)), J1*(Jr−1(E)). This is accomplished by defining an appropriate Poincaré–Cartan form. This form is also required in the definition of the associated symmetry problem and in the explicit construction of the Noether currents.