For a long time, it is generally believed that spin-spin interactions canonly exist in a theory where Lorentz symmetry is gauged, and a theory withspin-spin interactions is not perturbatively renormalizable. But this is nottrue. By studying the motion of a spinning particle in gravitational field, itis found that there exist spin-spin interactions in gauge theory of gravity.Its mechanism is that a spinning particle will generate gravitomagnetic fieldin space-time, and this gravitomagnetic field will interact with the spin ofanother particle, which will cause spin-spin interactions. So, spin-spininteractions are transmitted by gravitational field. The form of spin-spininteractions in post Newtonian approximations is deduced. This result can alsobe deduced from the Papapetrou equation. This kind of interactions will notaffect the renormalizability of the theory. The spin-spin interactions willviolate the weak equivalence principle, and the violation effects aredetectable. An experiment is proposed to detect the effects of the violation ofthe weak equivalence principle.
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