Gravitomagnetic Moments of the Fundamental Fields
  The quadratic form of the Dirac equation in a Riemann spacetime yields a gravitational gyromagnetic ratio \kappa_S = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio \kappa_S = 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. 
R. Aldrovandi, V. C. de Andrade and J. G. Pereira (IFT-UNESP, Sao   Paulo, Brazil)