# Path-integral derivation of the equations of the anomalous Hall effect

@article{Fujikawa2022PathintegralDO, title={Path-integral derivation of the equations of the anomalous Hall effect}, author={Kazuo Fujikawa and Koichiro Umetsu}, journal={Physical Review B}, year={2022} }

A path integral (Lagrangian formalism) is used to derive the eﬀective equations of motion of the anomalous Hall eﬀect with Berry’s phase on the basis of the adiabatic condition | E n ± 1 − E n | ≫ 2 π ~ /T , where T is the typical time scale of the slower system and E n is the energy level of the fast system. In the conventional deﬁnition of the adiabatic condition with T → large and ﬁxed energy eigenvalues, no commutation relations are deﬁned for slower variables by the Bjorken-Johnson-Low…

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