Denis Dalmazi | Searcharxiv

arXiv2021

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

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 $e_{μν}$ and a mixed symmetry tensor $B^{μ[αβ]}$. 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.

hep-th↗

arXiv2017

Massive spin-2 particles in a curved background via a nonsymmetric tensor

Massive spin-2 particles has been a subject of great interest in current research. If the graviton has a small mass, the gravitational force at large distances decreases more rapidly, which could contribute to explain the accelerated expansion of the universe. The massive spin-2 particles are commonly described by the known Fierz-Pauli action which is formulated in terms of a symmetric tensor $h_{μν}=h_{νμ}$. However, the Fierz-Pauli theory is not the only possible description of massive spin-2 particles via a rank-2 tensor. There are other two families of models $\mathcal{L}(a_1)$ and $\mathcal{L}_{nFP}(c)$, where $a_1$ and $c$ are real arbitrary parameters, which describe massive particles of spin-2 in the flat space via a nonsymmetric tensor $e_{μν}\neq e_{νμ}$. In the present work we derive Lagrangian constraints stemming from $\mathcal{L}(a_1)$ and $\mathcal{L}_{nFP}(c)$ in curved backgrounds with nonminimal couplings which are analytic functions of $m^2$. We show that the constraints lead to a correct counting of degrees of freedom if nonminimal terms are included with fine tuned coefficients and the background space is of the Einstein type, very much like the Fierz-Pauli case. We also examine the existence of local symmetries.

hep-th↗