Comments About Hamiltonian Formulation of Non-Linear Massive Gravity with Stuckelberg Fields

TL;DR

This paper analyzes the Hamiltonian structure of a gauge-invariant non-linear massive gravity action formulated with Stueckelberg fields. It identifies a primary constraint arising from the singularity condition $det V^{AB}=0$, which could prohibit an additional scalar ghost mode, while noting that the full 4D constraint algebra is intractable due to this singularity. In two dimensions, the authors successfully derive and verify the constraint algebra, showing ghost freedom consistent with prior work on gauge-fixed versions. The study highlights the challenges of extending the ghost-free structure to four dimensions and outlines concrete directions for completing the 4D analysis and broadening the Stueckelberg framework.

Abstract

We perform the Hamiltonian analysis of some form of the non-linear massive gravity action that is formulated in the Stuckelberg formalism. Following seminal analysis performed in arXiv:1203.5283 [hep-th] we find that this theory possesses one primary constraint which could eliminate one additional mode in this theory. We performed the explicit Hamiltonian analysis of two dimensional non-linear massive gravity and we found that this is theory free from the ghosts.