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Nonminimal coupling, equivalence principle and exact Foldy-Wouthuysen transformation

A. Accioly·H. Blas·H. Mukai
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Abstract

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.

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A. Accioly, H. Blas, H. Mukai. 2002-02-02. Nonminimal coupling, equivalence principle and exact Foldy-Wouthuysen transformation. https://arxiv.org/abs/gr-qc/0202006

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