Abstract: In the presence of a magnetic field，the momentum can be classified into mechanical and canonical

one，where the mechanical momentum corresponds to the velocity，and quantum mechanics has seldem introduced

the transport operator via the mechanical momentum. When the AB effect is discussed，the dynamical method is

uaually invoked. Once the transport operator is formed and is taken round the trips circuiting the magnetic field，AB

effect is reproduced. Our method explicitly exhibits the geometrical nature of the AB effect.

Key words: mechanical mometum, transport opertor, AB effect