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The pseudo-PT symmetric Dirac equation is proposed and analyzed by using anon-unitary Foldy-Wouthuysen transformations. A new spin operator PT symmetricexpectation value (called the mean spin operator) for an electron interactingwith a time-dependent electromagnetic field is obtained. We show that spinmagnetization - which is the quantity usually measured experimentally - is notdescribed by the standard spin operator but by this new mean spin operator toproperly describe magnetization dynamics in ferromagnetic materials and thecorresponding equation of motion is compatible with the phenomenological modelof the Landau-Lifshitz-Gilbert equation (LLG).

Pseudo-PT symmetric Dirac equation : effect of a new mean spin angular momentum operator on Gilbert damping