Hamiltonian analysis and positivity of a new massive spin-2 model

TL;DR

This paper analyzes a new model for massive spin-2 particles using Hamiltonian methods, confirming it describes the correct degrees of freedom and establishing its duality with the Fierz-Pauli theory.

Contribution

It provides a Hamiltonian analysis of a novel spin-2 model, demonstrating its degrees of freedom, positivity, and duality with Fierz-Pauli theory.

Findings

The model has 5 degrees of freedom in 4D, matching physical expectations.

Positivity of the Hamiltonian is established using spin projection operators.

A parent action shows the duality with Fierz-Pauli theory.

Abstract

Recently a new model has been proposed to describe free massive spin-2 particles in $D$ dimensions in terms of a non symmetric rank-2 tensor $e_{\mu\nu}$ and a mixed symmetry tensor $B^{\mu[\alpha\beta]}$. The model is invariant under linearized diffeomorphisms without Stueckelberg fields. It resembles a spin-2 version of the topologically massive spin-1 BF model (Cremmer-Scherk model). Here we apply the Dirac-Bergmann procedure in order to identify all Hamiltonian constraints and perform a complete counting of degrees of freedom. In $D=3+1$ we find 5 degrees of freedom corresponding to helicities $\pm{2}$, $\pm{1}$, $0$ as expected. The positivity of the reduced Hamiltonian is proved by using spin projection operators. We have also proposed a parent action that establishes the duality between the Fierz-Pauli and the new model. The equivalence between gauge invariant correlation functions of both theories is demonstrated.