BRST formalism for systems with higher order derivatives of gauge parameters

TL;DR

This paper proves the equivalence of Lagrangian and Hamiltonian BRST formalisms for systems with gauge transformations involving higher derivatives, clarifying the relation between different ghost formalisms.

Contribution

It establishes a formal connection between Lagrangian and Hamiltonian BRST approaches for higher-derivative gauge systems, including explicit relations for gauge-fixing terms.

Findings

Proves equivalence of BRST formalisms for higher derivative gauge systems

Relates BFV ghosts to Lagrangian ghosts and antighosts

Provides explicit gauge-fixing term relations

Abstract

For a wide class of mechanical systems, invariant under gauge transformations with higher (arbitrary) order time derivatives of gauge parameters, the equivalence of Lagrangian and Hamiltonian BRST formalisms is proved. It is shown that the Ostrogradsky formalism establishes the natural rules to relate the BFV ghost canonical pairs with the ghosts and antighosts introduced by the Lagrangian approach. Explicit relation between corresponding gauge-fixing terms is obtained.