Origin of Antifields in the Batalin-Vilkovisky Lagrangian Formalism

TL;DR

This paper explains the origin of antifields in the Batalin-Vilkovisky formalism, linking them to antighosts of collective fields that ensure gauge symmetry and Schwinger-Dyson equations are satisfied.

Contribution

It clarifies the conceptual origin of antifields as antighosts of collective fields and derives the associated antibracket structure from integrating out ghost fields.

Findings

Antifields are identified as antighosts of collective fields.

The antibracket structure emerges naturally from the formalism.

The Master Equation ensures correct Schwinger-Dyson equations.

Abstract

The antifields of the Batalin-Vilkovisky Lagrangian quantization are standard antighosts of certain collective fields. These collective fields ensure that Schwinger-Dyson equations are satisfied as a consequence of the gauge symmetry algebra. The associated antibracket and its canonical structure appear naturally if one integrates out the corresponding ghost fields. An analogous Master Equation for the action involving these ghosts follows from the requirement that the path integral gives rise to the correct Schwinger-Dyson equations.