Connection, horizontal lift, and berry phase

[wdlang]

i am now reading the PRL paper by simon on berry phase

under adiabatic approximation, the wave function evolves as

\langle \psi | d/dt | \psi \rangle=0.

how to relate this equation to the connection on a fiber bundle?

how to understand that the wave function is parallel transported?

 

[element4]

Your questions are answered in http://pra.aps.org/abstract/PRA/v43/i3/p1206_1" .

 

[wdlang]

Your questions are answered in http://pra.aps.org/abstract/PRA/v43/i3/p1206_1" .

thanks a lot

i will have a look