Assuming that $h_{ab}$ is some metric perturbation and $h_{<ab>}$ means the traceless part, I have the LHS of the next equation and I want to find a field redefinition $t_{ab}$ as a function of $h$ and $h_{ab}$ such that I can rewrite the expression as the last line : $$E_{<ab>}= ( \Box+m_1^2) ( \Box+m_2^2) \Box h_{<ab>}+ ( \Box+m_3^2) ( \Box+m_4^2) \partial_{<a}\partial_{b>}h = ^{?} ( \Box+M_1^2) ( \Box+M_2^2) ( \Box+M_3^2) t_{ab} $$ Exist some particular method to do it? ( $h=h_{ab}g^{ab}$ is simply the trace of $h_{ab}$ and $g_{ab}$ is the background / zero order metric. ) Thanks.


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