A note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields

Abstract

It is possible to show that there are three independent families of models describing a massive spin-2 particle via a rank-2 tensor. One of them contains the massive Fierz-Pauli model, the only case described by a symmetric tensor. The three families have different local symmetries in the massless limit and can not be interconnected by any local field redefinition. We show here however, that they can be related with the help of a decoupled and non dynamic (spectator) field. The spectator field may be either an antisymmetric tensor $B_{\mu \nu }=-B_{\nu \mu }$, a vector $A_{\mu }$ or a scalar field $\phi$, corresponding to each of the three families. The addition of the extra field allows us to formulate master actions which interpolate between the symmetric Fierz-Pauli theory and the other models. We argue that massive gravity models based on the Fierz-Pauli theory are not expected to be equivalent to possible local self-interacting theories built up on the top of the two new families of massive spin-2 models. The approach used here may be useful to investigate dual (nonsymmetric) formulations of higher spin particles.

9 pages, no figures

References in corpus (6)

• Resummation of Massive Gravity
• Massive Gravity in Three Dimensions
• Dual Massive Gravity
• A note on linearized "New Massive Gravity" in arbitrary dimensions
• Massive spin-2 particle from a rank-2 tensor
• Nonuniqueness of the Fierz-Pauli mass term for a nonsymmetic tensor

Cited by in corpus (5)

• Classical and quantum theory of the massive spin-two field
• Massive "spin-2" theories in arbitrary $D\ge 3$ dimensions
• Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion
• Self-dual models in $D=2+1$ from dimensional reduction
• Absence of the Higuchi bound in a family of alternative linear massive spin-2 models