Cohomology of the infinite-order jet space and the inverse problem

Abstract

Cohomology of the bicomplex of exterior forms on the infinite-order jet space of a smooth fiber bundle of a field model is computed. This provides a solution of the global inverse problem of the calculus of variations in Lagrangian field theory and time-dependent mechanics. In the case of an affine fiber bundle, the outcomes to BRST theory are discussed. We show that there is no topological obstruction to constructing global descent equations in the even field sector of BRST theory.