Abstract
We quantitatively formulate the nonadiabatic non-Abelian geometric phase by generalizing the Lewis invariant method to a degenerate case, which is reduced to Wilczek and Zee's [Phys. Rev. Lett. 52, 2111 (1984)] non-Abelian geometric phase in the adiabatic limit. We also derive the effective propagator accommodating the nonadiabatic non-Abelian geometric phase and the semiclassical quantization rule in the adiabatic limit.
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