Ay. Trifonov et Aa. Yevseyevich, MASLOVS COMPLEX GERM METHOD AND BERRYS PHASE, Journal of physics. A, mathematical and general, 27(18), 1994, pp. 6267-6286
In the adiabatic approximation the connection of the Berry phase with
the quasiclassical trajectory-coherent states of the Schrodinger-type
equation (with the arbitrary scalar (h) over bar-(pseudo) differential
operator) and the Dirac equation in the external periodic electromagn
etic field is studied.