First-class constraints and the BV formalism

TL;DR

This paper introduces a BV formalism-based method to derive first-class constraints, including the Hamiltonian constraint, without canonical momentum calculations, offering a Lagrangian perspective for constrained systems.

Contribution

It provides a systematic, simple prescription within the BV formalism to obtain constraints, enhancing the Lagrangian approach to constrained systems and highlighting an analogy with antifields.

Findings

Derives first-class constraints without computing canonical momenta.

Simplifies the process of obtaining the Hamiltonian constraint.

Establishes an analogy between antifields and first-class constraints.

Abstract

Employing the Batalin-Vilkovisky (BV) formalism, we present a systematic and simple prescription to derive (first-class) constraints including the Hamiltonian constraint (a.k.a. flow equation), which plays pivotal role in holographic computation of Weyl anomalies. In this method, you do not have to compute canonical momenta nor Hamiltonians. Thus it may equip us with a `Lagrangian treatment' of constrained systems. We also point out an interesting analogy between antifields and first-class constraints.