  The spin dynamics in constant electromagnetic fields is described by the
Bargmann-Michel-Telegdi equation which can be upgraded with anomalous magnetic
and electric dipole moments. The upgraded equation remains self-consistent,
Lorentz-covariant and gauge-invariant. It and its different forms have been
confirmed in numerous experiments to high degree of accuracy. We have recently
derived the spin motion equation within the Wentzel-Kramers-Brillouin
weak-field approximation which adds a pseudoscalar correction to the BMT
equation. The upgraded equation is again self-consistent, Lorentz-covariant,
gauge-invariant, and free of unwanted artifacts. The pseudoscalar correction is
expected to be small, and might become important in hypersensitive experiments,
like the measurements of electric dipole moments which are themselves related
to pseudoscalar quantities. It also becomes possible to explain why EDMs are so
difficult to measure, since this correction term might lead to the effective
screening of electric dipole moments. Within the same model, it is possible to
explain the discrepancy between experimental and theoretical values of muon
magnetic anomaly under assumption that the pseudoscalar correction is the
dominant source of this discrepancy.
