Field theory of anyons and the fractional quantum Hall effect

We present a microscopic theory of the fractional quantum Hall effect and its hierarchy structure on the basis of a Chern-Simons gauge theory. It is shown field theoretically that the system of the planar electrons in a strong magnetic field yields a hierarchy of the fractional quantum Hall states, which are a condensed phase of the bosonized electrons and vortices. It is discussed in detail how the Coulomb interaction between electrons plays a crucial role in this phenomenon.