The Orbital Gyromagnetic Factor of Relativistic Electrons

An analog of the Bargmann-Michel-Telegdi (BMT) equation which describes the motion of the spin four-vector S is derived for the orbital magnetic moment L. It is shown that in addition to the term in dL/dt describing the precession of the orbital angular momentum in a magnetic field, there appears a term which may imply the possibility of an anomalous contribution to the orbital g-factor g$_{L}$. Experiments to measure the anomaly are discussed.