From Hamiltonian to Lagrangian Sp(2) BRST Quantization

TL;DR

This paper formally proves the equivalence between Hamiltonian and Lagrangian BRST quantization for Sp(2)-symmetric theories, introducing a new quantum master equation in the Hamiltonian framework that encompasses all relevant fields and momenta.

Contribution

It provides a rigorous proof of the equivalence between Hamiltonian and Lagrangian BRST quantization for Sp(2) theories and derives a novel quantum master equation in the Hamiltonian setting.

Findings

Formal proof of equivalence between Hamiltonian and Lagrangian BRST quantization.

Derivation of a new quantum master equation in Hamiltonian formalism.

Applicability to generic Sp(2)-symmetric theories using Darboux coordinates.

Abstract

We give a formal proof of the equivalence of Hamiltonian and Lagrangian BRST quantization. This is done for a generic $Sp(2)$-symmetric theory using flat (Darboux) coordinates. A new quantum master equation is derived in a Hamiltonian setting which contains all the Hamiltonian fields and momenta of a given theory.