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

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.

arXiv comment18 pages, 0 figures

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