Variation Bicomplex

In mathematics, the Lagrangian theory is formulated on smooth bundles in algebraic form in terms of a variational bicomplex , without appeal to the calculus of variations . For example, this applies to classical field theory .

A variational bicomplex is a cochain complex of a differential graded algebra on a manifold of jets of sections of a smooth bundle. Lagrangians and Euler - Lagrange operators on bundles are defined algebraically as elements of this bicomplex. The cohomology of the variational bicomplex leads to the global first variational formula and the first Noether theorem .

Being generalized to the Lagrangian theory of graded even and odd variables on graded manifolds, the variational bicomplex allows us to give a rigorous mathematical formulation of the classical field theory in the general case of reduced degenerate BRST theory of Lagrangians.