The KT-BRST complex of a degenerate Lagrangian system

TL;DR

This paper constructs the KT-BRST complex for degenerate Lagrangian systems, enabling the systematic identification of gauge symmetries and Noether identities, and facilitating the extension of the Lagrangian to a proper master action.

Contribution

It introduces a method to associate a KT-BRST complex with degenerate Lagrangians, clarifying the selection of non-trivial Noether identities and gauge symmetries.

Findings

The KT-BRST complex encodes all non-trivial Noether identities.

The method allows extending the Lagrangian to a proper solution of the master equation.

Provides a systematic approach for quantization of degenerate Lagrangian systems.

Abstract

Quantization of a Lagrangian field system essentially depends on its degeneracy and implies its BRST extension defined by sets of non-trivial Noether and higher-stage Noether identities. However, one meets a problem how to select trivial and non-trivial higher-stage Noether identities. We show that, under certain conditions, one can associate to a degenerate Lagrangian L the KT-BRST complex of fields, antifields and ghosts whose boundary and coboundary operators provide all non-trivial Noether identities and gauge symmetries of L. In this case, L can be extended to a proper solution of the master equation.