On Local Variational Differential Operators in Field Theory

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.