  In this paper we study the Aharonov-Bohm (A-B) effect and Anderson-Higgs
mechanism in Ginzburg-Landau model of superconductors from the perspective of
the decomposition of U(1) gauge potential. By the Helmholtz theorem, we derive
exactly the expression of the transverse gauge potential $\vec{A}_\perp$ in A-B
experiment, which is gauge-invariant and physical. For the case of a bulk
superconductor, we find that the gradient of the total phase field $\theta$
provides the longitudinal component ${\vec A}_{\parallel}$, which reflects the
Anderson-Higgs mechanism. For the case of a superconductor ring, the gradient
of the longitudinal phase field $\theta_1$ provides the longitudinal component
${\vec A}_{\parallel}$, while the transverse phase field $\theta_2$ produces
new physical effects such as the flux quantization inside a superconducting
ring.
