Superfield generating equation of field–antifield formalism as a hyper-gauge theory

Within a superfield approach, we formulate a simple quantum generating equation of the field–antifield formalism. Then we derive the Schroedinger equation with the Hamiltonian whose Δ -exact part serves as a generator to the quantum master transformations. We show that these generators do satisfy a nice composition law in terms of the quantum antibrackets. We also present an Sp (2) symmetric extension to the main construction, with specific features caused by the principal fact that all basic equations become Sp (2) vector-valued ones.