Coherent state representation approach to fractional quantum hall effect

Abstract

The fractional quantum Hall effect is studied by using the coherent path integral technique. By introducing the Chern-Simons term into the Lagrangian, the electrons in the system become attached to the Chem-Simons flux quanta resulting in a system of composite particles and the phenomenon of statistical transmutation. In this thesis, we use the mean field approach in which the method of integer quantum Hall effect can be applied only when the filling factor takes the form 1/(2p+1) with p being an arbitrary positive integer related to the coefficient of the Chern-Simons term in the Lagrangian. It is also found that the Hall conductivity is given by 1/(2p+1) multiplied by the electron charge and Planck's constant.