Fractional Quantum Hall Effect

This thesis captures the progress on Fractional Quantum Hall Effect based on the Ginsburg-Landau Chern-Simons field theoretical approach, i.e. theory that proceed from microscopic electronic Hamiltonian to the final solution via a sequence of transformations and approximations. The detailed theoretical review of the fractional quantised Hall Effect includes both the trial wave function approaches which were forwarded by Laughlin and Jian, and the field theoretical approaches which were forwarded by Lopez and Fradkin. The Ginsburg-Landau Chiron-Simons field theoretical approach, in which electrons are converted to Chiron-Simons composite bosons that carry attached flux tubes, is considered as a better theoretical approach to explain different phenomena of fractional quantum Hall effect.