Nonuniqueness of the Fierz-Pauli mass term for a nonsymmetic tensor

Abstract

Starting with a description of massive spin-2 particles in D = 4 in terms of a mixed symmetry tensor T-[mu nu]rho without a totally antisymmetric part (T-[[mu nu]rho] = 0), we obtain a dual model in terms of a non-symmetric tensor e(mu nu). The model is of second order in derivatives, and its mass term (e(mu nu)e(nu mu) + ce(2)) contains an arbitrary real parameter c. Remarkably, it is free of ghosts for any real value of c and describes a massive spin-2 particle as expected from duality. The antisymmetric part e([mu nu]) plays the role of auxiliary fields, vanishing on shell. In the massless case the model describes a massless spin-2 particle without ghosts. DOI: 10.1103/PhysRevD.86.125036