Note About Hamiltonian Formalism for General Non-Linear Massive Gravity Action in Stuckelberg Formalism

TL;DR

This paper investigates the Hamiltonian structure of non-linear massive gravity in Stuckelberg formalism, aiming to demonstrate the absence of ghosts and analyze the constraint system, though some stability aspects remain unresolved.

Contribution

It provides a detailed Hamiltonian analysis of non-linear massive gravity in Stuckelberg formalism, identifying primary constraints and exploring ghost-free conditions.

Findings

Constraint structure can eliminate non-physical modes

Hamiltonian form derived for general non-linear massive gravity

Complete stability analysis remains incomplete due to complex constraints

Abstract

In this note we try to prove the absence of the ghosts in case of the general non-linear massive gravity action in Stuckelberg formalism. We argue that in order to find the explicit form of the Hamiltonian it is natural to start with the general non-linear massive gravity action found in arXiv:1106.3344 [hep-th]. We perform the complete Hamiltonian analysis of the Stuckelberg form of the minimal the non-linear gravity action in this formulation and show that the constraint structure is so rich that it is possible to eliminate non-physical modes. Then we extend this analysis to the case of the general non-linear massive gravity action. We find the corresponding Hamiltonian and collection of the primary constraints. Unfortunately we are not able to finish the complete analysis of the stability of all constraints due to the complex form of one primary constraint so that we are not able to determine the conditions under which given constraint is preserved during the time evolution of the system.