Understand
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.