Superfield generating equation of field-antifield formalism

TL;DR

This paper introduces a quantum superfield generating equation within the field-antifield formalism, extending it with an $Sp(2)$ symmetry and highlighting the role of quantum antibrackets in the Heisenberg equations.

Contribution

It presents a new superfield generating equation, extends the formalism with $Sp(2)$ symmetry, and emphasizes the significance of quantum antibrackets in the Heisenberg equations.

Findings

Derivation of a Schrödinger equation with a $ riangle$-exact Hamiltonian.

Development of an $Sp(2)$ symmetric extension of the formalism.

Demonstration of the role of quantum antibrackets in Heisenberg equations.

Abstract

A simple quantum superfield generating equation of the field-antifield formalism is proposed. The Schroedinger equation with the Hamiltonian having $\Delta$-exact form is derived. 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, is presented. A principal role of quantum antibrackets in formulation of the Heisenberg equations of motion is shown.