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[μν]ρ without a totally antisymmetric part (T[[μν]ρ]=0), we obtain a dual model in terms of a nonsymmetric tensor eμν. The model is of second order in derivatives, and its mass term (eμνeνμ+ce2) 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[μν] plays the role of auxiliary fields, vanishing on shell. In the massless case the model describes a massless spin-2 particle without ghosts. © 2012 American Physical Society.