Quantum Sp(2)-antibrackets and open groups

TL;DR

This paper extends the concept of quantum antibrackets to the Sp(2) formalism, introducing generalized brackets and master equations that incorporate higher structures and are applicable to open groups.

Contribution

It generalizes quantum antibrackets to the Sp(2) setting and develops new quantum master equations involving higher Sp(2)-antibrackets for open groups.

Findings

True quantum versions of classical Sp(2)-antibrackets for commuting operators

Generalized bracket structures with higher Sp(2)-antibrackets for arbitrary operators

Quantum master equations incorporating Sp(2)-brackets and open group structures

Abstract

The recently presented quantum antibrackets are generalized to quantum Sp(2)-antibrackets. For the class of commuting operators there are true quantum versions of the classical Sp(2)-antibrackets. For arbitrary operators we have a generalized bracket structure involving higher Sp(2)-antibrackets. It is shown that these quantum antibrackets may be obtained from generating operators involving operators in arbitrary involutions. A recently presented quantum master equation for operators, which was proposed to encode generalized quantum Maurer-Cartan equations for arbitrary open groups, is generalized to the Sp(2) formalism. In these new quantum master equations the generalized Sp(2)-brackets appear naturally.