Nonminimal coupling, equivalence principle and exact Foldy-Wouthuysen transformation

Abstract

It is shown that the exact Foldy-Wouthuysen transformation for spin-0 particles on spacetimes described by the metrics $d{s}^2=V^{2}d{t}^2-W^{2}d{\mathbf{x}}^2$, where $V=V(\mathbf{x})$ and $W=W(\mathbf{x})$, 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.

9 pages, LaTex