We show that covariant field theory for sections of π : lifts in a natural way to the bundle of vertically adapted linear frames Our analysis is based on the fact that is a principal fiber bundle over the bundle of 1-jets On the canonical soldering 1-forms play the role of the contact structure of A lifted Lagrangian ℒ: is used to construct modified soldering 1-forms, which we refer to as the Cartan–Hamilton–Poincaré 1-forms. These 1-forms on pass to the quotient to define the standard Cartan–Hamilton–Poincaré -form on We derive generalized Hamilton–Jacobi and Hamilton equations on and show that the Hamilton–Jacobi and canonical equations of Carathéodory–Rund and de Donder–Weyl are obtained as special cases.
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