The antifield Koszul-Tate complex of reducible Noether identities

TL;DR

This paper develops an algebraic framework using the antifield Koszul-Tate complex to analyze the hierarchy of Noether identities in degenerate Lagrangian systems, facilitating their BV quantization.

Contribution

It introduces a condition under which an exact Koszul-Tate complex can be constructed for reducible Noether identities in degenerate Lagrangian systems.

Findings

Constructs the antifield Koszul-Tate complex for reducible Noether identities.

Shows the complex's boundary operator encodes all Noether and higher-stage identities.

Provides a foundation for BV quantization of degenerate Lagrangian systems.

Abstract

A generic degenerate Lagrangian system of even and odd fields is examined in algebraic terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. We show that, if a certain necessary and sufficient condition holds, one can associate to a degenerate Lagrangian system the exact Koszul-Tate complex with the boundary operator whose nilpotency condition restarts all its Noether and higher-stage Noether identities. This complex provides a sufficient analysis of the degeneracy of a Lagrangian system for the purpose of its BV quantization.