Schwinger-Dyson BRST-Symmetry and the Equivalence of Hamiltonian and Lagrangian Quantistion

TL;DR

This paper demonstrates the equivalence of Hamiltonian and Lagrangian BRST formalisms in quantum field theory by leveraging Schwinger-Dyson BRST symmetry, deriving the quantum master equation from Hamiltonian principles.

Contribution

It establishes a direct connection between Hamiltonian and Lagrangian BRST quantization, showing their equivalence at the path integral level using Schwinger-Dyson symmetry.

Findings

Hamiltonian and Lagrangian BRST formalisms are equivalent.

The quantum master equation is derived from Hamiltonian BRST quantization.

The approach confirms the consistency of BRST symmetry across formalisms.

Abstract

Implementing the requirement that a field theory be invariant under Schwinger-Dyson BRST symmetry in the Hamiltonian formalism, we show the equivalence between Hamiltonian and Lagrangian BRST-formalism at the path integral level. The Lagrangian quantum master equation is derived as a direct consequence of the Fradkin-Vilkovisky theorem in Hamiltonian BRST quantisation.