Fractional charge in quantum Hall effect
  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. 
Keshav N. Shrivastava