Abstract
The quadratic form of the Dirac equation in a Riemann spacetime yields a gravitational gyromagnetic ratio κ_S = 2 for the interaction of a Dirac spinor with curvature. A gravitational gyromagnetic ratio κ_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.
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