Post-Newtonian effects of Dirac particle in curved spacetime - II : the electron g-2 in the Earth's gravity

The general relativistic effects to the anomalous magnetic moment of the electron ${\rm g}_{\rm e}$-2 in the Earth's gravitational field have been examined. The magnetic moment of electrons to be measured on the Earth's surface is evaluated as $\mu_{\rm m}^{\rm eff} \simeq (1\!+\!3\phi/c^2)\,\mu_{\rm m}$ on the basis of the Dirac equation containing the post-Newtonian effects of the general relativity for fermions moving in the Earth's gravitational field. This implies that the anomalous magnetic moment of $10^{-9}$ appears in addition to the radiative corrections in the quantum field theory. This may seem contradictory with the fact of the 12th digit agreement between the experimental value measured on the ground level ${\rm g}_{\rm e(EXP)}$ and the theoretical value calculated in the flat spacetime ${\rm g}_{\rm e(SM)}$. In this paper, we show that the apparent contradiction can be explained consistently with the framework of the general relativity.