Generalized Lagrangian Master Equations

TL;DR

This paper explores the geometric structure of Lagrangian quantization using BRST symmetries, extending the Batalin-Vilkovisky formalism to more general measures and emphasizing the importance of a natural connection on the field space.

Contribution

It introduces a generalized geometric framework for Lagrangian quantization that unifies BRST symmetries with the Batalin-Vilkovisky formalism under broader conditions.

Findings

Revealed the role of a natural connection on the space of fields.

Extended the Batalin-Vilkovisky formalism to arbitrary measures.

Connected ghost fields integration with geometric structures.

Abstract

We discuss the geometry of the Lagrangian quantization scheme based on (generalized) Schwinger-Dyson BRST symmetries. When a certain set of ghost fields are integrated out of the path integral, we recover the Batalin-Vilkovisky formalism, now extended to arbitrary functional measures for the classical fields. Keeping the ghosts reveals the crucial role played by a natural connection on the space of fields.