The spin precession of an electron in an external electromagnetic field is described by the Bargmann–Michel–Telegdi (BMT) equation 
where , , , and  are polarization four-vector, charge, mass, and magnetic moment,  is four-velocity of electron (in a system of units in which ), , , and  is electromagnetic field-strength tensor. Using equations of motion,
one can rewrite the first term on the right side of the BMT equation as , where  is four-acceleration. This term describes Fermi–Walker transport and leads to Thomas precession. The second term is associated with Larmor precession.
When electromagnetic fields are uniform in space or when gradient forces like  can be neglected, the particle's translational motion is described by
The BMT equation is then written as 
The Beam-Optical version of the Thomas-BMT, from the Quantum Theory of Charged-Particle Beam Optics, applicable in accelerator optics