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

Abstract: 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 $\Delta$ - 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 as to the main construction, with specific features caused with the principal fact that all basic equations become $Sp(2)$ vector valued ones.