What is spin-magnetic moment of electron?

Abstract We investigate the problem about what the spin-magnetic moment is. The magnetic moment of the Dirac electron in the frame along z -axis is evaluated. This is identified with the spin-magnetic moment of the electron, because there is not any z -component of magnetic moment caused by orbital angular momentum in our frame. The correct value of the spin-magnetic moment and the correct ratio of the spin-magnetic moment to the spin (i.e. g = 2 ) are obtained explicitly. In deriving them, the negative energy solutions of the Dirac equation perform essential roles. We find that the transition current from a positive energy state to a negative energy state causes spin-magnetic moment of the electrons in vacuum. This fact implies that the ratio of the spin-magnetic moment to the spin may change depending on the environments. For example, it may have different values in materials.