Magus found a force on a spinning particle. It is a lift force that acts along a direction perpendicular to the particle linear velocity and its rotational velocity. Does it have a quantum analogue? Does it have relativistic analogue?
Rotation is usually not well treated, even in Classic Mechanics. A force is defined through the inertial mass when the motion of a material body changes. This is clear with translational motion. Material body have an arrangement, which can we represented by an orthonormal basis and its rotation with respect to a fixed basis. The instantaneous rotational motion is defined by the inverse of the rotation x the derivative of the rotation, it does not depend on the choice of a basis and can be represented by a vector (up to a sign, which gives the spin, which has nothing to do with QM). The extension of momentum gives the rotational momentum, and d the concept of torques, which are different objects then mass and forces. We must accept that all material bodies, including elementary particles, have some arrangement, and then can have an instantaneous rotational motion. Then we have both forces and torques.
The extension to the relativist geometry is possible, but requires a more elaborated mathematical framework. See my book Theoretical Physics, chap 4. Their quantization follows general rules.
Perhaps the best analyses of relativistic forces come from the studies of neutron stars, which are in effect super-massive objects where extreme rates of spin take the surface speed up to 0.25C.
Try 'Gravitational waves from rotating neutron stars' by D I Jones for a good overview.
The more detailed research that I read doesn't really investigate the force relationships but tend to focus on the mechanisms for creating and maintaining spin with the massive energy loss required to overcome super-magnetic moment.
I may just have been too selective in my search criteria.
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