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

## TL;DR

This paper develops a superfield-based quantum generating equation within the field-antifield formalism, introducing an $Sp(2)$ symmetric extension and analyzing the algebraic structure of quantum master-transformations.

## Contribution

It formulates a new superfield quantum generating equation for the field-antifield formalism and extends it to include an $Sp(2)$ symmetric version with vector-valued equations.

## Key findings

- Derived a Schrödinger equation with a $ riangle$-exact Hamiltonian component.
- Showed that quantum master-transformations satisfy a composition law via quantum antibrackets.
- Presented an $Sp(2)$ symmetric extension with vector-valued equations.

## 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.