  The low-lying excitations of a quantum Hall state on a disk geometry are edge
excitations. Their dynamics is governed by a conformal field theory on the
cylinder defined by the disk boundary and the time variable. We give a simple
and detailed derivation of this conformal field theory for integer filling,
starting from the microscopic dynamics of $(2+1)$-dimensional non-relativistic
electrons in Landau levels. This construction can be generalized to describe
Laughlin's fractional Hall states via chiral bosonization, thereby making
contact with the effective Chern-Simons theory approach. The conformal field
theory dictates the finite-size effects in the energy spectrum. An experimental
or numerical verification of these universal effects would provide a further
confirmation of Laughlin's theory of incompressible quantum fluids.
