Nonminimal coupling, equivalence principle and exact Foldy-Wouthuysen transformation

It is shown that the exact Foldy-Wouthuysen transformation for spin-0 particles on spacetimes described by the metrics $ds^2 = V^2 dt^2 - W^2 d {\bf{x}}^2$,where$V=V({\bf{x}})$and$W=W({\bf{x}})$, only exists if the scalar field is nonminimally coupled to the Ricci scalar field with a coupling constant equal to 1/6. The nonminimal coupling term, in turn, does not violate the equivalence principle. As an application we obtain the nonrelativistic Foldy-Wouthuysen Hamiltonian concerning the general solution to the linearized field equations of higher-derivative gravity for a static pointlike source in the Teyssandier gauge.