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A note on the nonuniqueness of the massive Fierz-Pauli theory and spectator fields
High Energy Physics - Theory · Submitted 3 Jul 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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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 $\varphi$, 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It is possible to show that there are three independent families of models describing a massive spin-2 particle via a rank-2 tensor. | result 0.52 | 0.35 | 0.12 | hedged possibility 0.84 |
| s1 | One of them contains the massive Fierz-Pauli model, the only case described by a symmetric tensor. | background 0.60 | 0.24 | 0.07 | asserted 1.00 |
| s2 | The three families have different local symmetries in the massless limit and can not be interconnected by any local field redefinition. | background 0.77 | 0.21 | 0.09 | asserted 1.00 |
| s3 | We show here however, that they can be related with the help of a decoupled and non dynamic (spectator) field. | contribution 0.57 | 0.92 | 0.50 | asserted 1.00 |
| s4 | The spectator field may be either an antisymmetric tensor $B_{\mu\nu}=-B_{\nu\mu}$, a vector $A_{\mu}$ or a scalar field $\varphi$, corresponding to each of the three families. | result 0.52 | 0.73 | 0.09 | asserted 0.53 |
| s5 | The addition of the extra field allows us to formulate master actions which interpolate between the symmetric Fierz-Pauli theory and the other models. | contribution 0.43 | 0.89 | 0.16 | asserted 0.86 |
| s6 | 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. | interpretation 0.96 | 0.49 | 0.64 | hedged possibility 0.93 |
| s7 | The approach used here may be useful to investigate dual (nonsymmetric) formulations of higher spin particles. | future work 0.98 | 0.21 | 0.05 | hedged possibility 1.00 |
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Original 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 $\varphi$, 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.
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1 arXiv paper cite this in 2 sentences
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Cites it as background 1 paper
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Although these have been subject of many works [ref] , usually only certain aspects of the theory of spin-two fields have been considered and a comprehensive review is still missing.
Classical and quantum theory of the massive spin-two field · Introduction · 0.86
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