Note that negative signs in the above expressions are because an electron carries negative charge, and the value of g S can be derived naturally from Dirac's equation. The total magnetic moment μ μ → → J , as a vector operator, does not lie on the direction of total angular momentum J → → = L → → + S → → , because the g-factors for orbital and spin part are different. However, due to Wigner-Eckart theorem, its expectation value does effectively lie on the direction of J → → which can be employed in the determination of the g -factor according to the rules of angular momentum coupling. In particular, the g -factor is defined as a consequence of the theorem itself