Proof of Consistency of Nonlinear Massive Gravity in the Stuckelberg Formulation

TL;DR

This paper proves the absence of the Boulware-Deser ghost in the nonlinear massive gravity theory using the Stuckelberg formulation, confirming its theoretical consistency at the nonlinear level.

Contribution

It provides a rigorous proof of ghost absence in the Stuckelberg formulation of nonlinear massive gravity, including explicit constraint calculations.

Findings

Confirmed the absence of the Boulware-Deser ghost at nonlinear level

Explicitly computed the constraints removing the ghost

Validated the consistency of the Stuckelberg formulation

Abstract

We address some recent concerns about the absence of the Boulware-Deser ghost in the Stuckelberg formulation of nonlinear massive gravity. First we provide general arguments for why any ghost analysis in the Stuckelberg formulation has to agree with existing consistency proofs that have been carried out without using Stuckelberg fields. We then demonstrate the absence of the ghost at the completely nonlinear level in the Stuckelberg formulation of the minimal massive gravity action. The constraint that removes the ghost field and the associated secondary constraint that eliminates its conjugate momentum are computed explicitly, confirming the consistency of the theory in the Stuckelberg formulation.