  Using the fact that the nonintegrable phase factor can reformulate the gauge
theory in terms of path dependent vector potentials, the quantization condition
for the nonintegrable phase is investigated. It is shown that the
path-dependent formalism can provide compact description of the flux
quantization and the charge quantization at the existence of a magnetic
monopole. Moreover, the path-dependent formalism gives suggestions for
searching of the quantized flux in different configurations and for other
possible reasons of the charge quantization. As an example, the developed
formalism is employed for a (1+1) dimensional world, showing the relationship
between the fundamental unit of the charge and the fine structure constant for
this world.
