Massive gravity, canonical structure and gauge symmetry

TL;DR

This paper performs a Hamiltonian analysis of massive gravity, demonstrating it is ghost-free and exploring the gauge symmetry structure, which is clarified through the Stuckelberg formulation.

Contribution

It provides a detailed Hamiltonian analysis showing the ghost-free nature of massive gravity and clarifies the gauge symmetry via the Stuckelberg approach.

Findings

Massive gravity is ghost-free in full phase space.

The absence of first class constraints indicates no apparent gauge symmetry.

Gauge symmetry becomes manifest in the Stuckelberg formulation.

Abstract

Performing Hamiltonian analysis of the massive gravity [9] in full phase space, we see that the theory is ghost free. We also see in a more clear way that this result is intrinsic of the interaction term and does not depend on the variables involved. Since no first class constraint emerges, the theory seems to lack gauge symmetry. We show that this is due to the presence of an auxiliary field, and the symmetry may be manifest in the Stuckelberg formulation. We give the generating functional of gauge transformation in this model.