Gravitomagnetic Moments of the Fundamental Fields

The quadratic form of the Dirac equation in a Riemann space–time yields a gravitational gyromagnetic ratio κS=2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio κS=1 is also found for the interaction of a vector field with curvature. It is shown that the Dirac equation in a curved background can be obtained as the square-root of the corresponding vector field equation only if the gravitational gyromagnetic ratios are properly taken into account.