Abstract
The Dirac equation is derived in the Foldy-Wouthuysen representation describing the interaction of spin-1/2 relativistic particles with an external electromagnetic field; it is valid in the weak-field approximation. In contrast to previous studies, this equation includes all of the order derivatives of the field potentials. The quantum-mechanical equation is obtained for the spin motion in the Foldy-Wouthuysen representation; it is consistent with the classical Bargmann-Michel-Telegdi equation.
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