Nonminimal coupling, equivalence principle and exact Foldy-Wouthuysen transformation

TL;DR

This paper demonstrates that an exact Foldy-Wouthuysen transformation for spin-0 particles in certain curved spacetimes exists only with a specific nonminimal coupling to gravity, which does not violate the equivalence principle, and applies it to higher-derivative gravity solutions.

Contribution

It establishes the necessity of a 1/6 nonminimal coupling for exact FW transformation in specific metrics and applies this to higher-derivative gravity solutions.

Findings

Exact FW transformation exists only with nonminimal coupling of 1/6.

Nonminimal coupling does not violate the equivalence principle.

Derived nonrelativistic Hamiltonian for higher-derivative gravity solutions.

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.