  We propose and develop a new calculus for local variational differential
operators. The main difference of the new formalism with the canonical
differential calculus is that the image of higher order operators on local
functionals does not contain indefinite quantities like $\delta(0)$. We apply
this formalism to BV formulation of general gauge field theory and to its
Sp(2)-symmetric generalization. Its relation to a quasiclassical expansion is
also discussed.
