We develop a new calculus for local variational differential operators where the action of higher-order operators on local functionals does not lead to indefinite quantities like δ(0). We apply this formalism to the Batalin-Vilkovisky formulation of local general gauge field theory and to its Sp(2)-symmetrical generalization. Its relation to a semiclassical expansion is also discussed.

The existence of a local solution to the Sp(2) master equation for the gauge field theory is proved in the perturbation theory under standard regularity assumptions for the action. The arbitrariness of solutions to the Sp(2) master equation is described, provided they are proper. The effective action can be chosen to be Sp(2) invariant and (under the additional assumption that the gauge transformation generators are Lorentz tensors) Lorentz invariant.