  In 1976 Jackiw and Rebbi found 1/2 of a fermion number by using Dirac
equation in 1+1 dimensions. Schrieffer in several proposals made an effort to
suggest that there is a fractional charge. The calculations of Peierls
distortion, Berry's phase and classical action were presented to accomodate the
fractional charge in non-relativistic theory. Laughlin used the antisymmetry to
define the charge density per unit area in a two dimensional system. In order
to elliminate the area, Laughlin introduced the incompressibility which fixed
the area so that the odd number, which determines the antisymmetry of the
electron wave function, gave the charge. We have used the orbital angular
momentum and the spin to define the charge, in full agreement with the quantum
Hall effect data.
