Abstract
Lorentz invariant derivative interactions for a single spin-2 field are investigated, up to the cubic order. We start from the most general Lorentz invariant terms involving two spacetime derivatives, which are polynomials in the spin-2 field as well as its first derivatives. Using a perturbative Arnowitt-Deser-Misner analysis, we determined the parameters such that the corresponding Hamiltonian possesses a Lagrange multiplier, which would signify there are at most 5 degrees of freedom that are propagating. The resulting derivative terms are linear combinations of terms coming from the expansion of the Einstein-Hilbert Lagrangian around a Minkowski background, as well as the cubic “pseudolinear derivative term” identified in Hinterbichler [J. High Energy Phys. 10 (2013) 102]. We also derived the compatible potential terms, which are linear combinations of the expansions of the first two de Rham–Gabadadze–Tolley mass terms in unitary gauge.
- Received 10 June 2014
DOI:https://doi.org/10.1103/PhysRevD.90.064024
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