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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