  Edge states of the quantum Hall fluid provide an almost unparalled
opportunity to study mesoscopic effects in a highly correlated electron system.
In this paper we develop a bosonization formalism for the finite-size edge
state, as described by chiral Luttinger liquid theory, and use it to study the
Aharonov-Bohm effect. The problem we address may be realized experimentally by
measuring the tunneling current between two edge states through a third edge
state formed around an antidot in the fractional quantum Hall effect regime. A
renormalization group analysis reveals the existence of a two-parameter
universal scaling function G(X,Y) that describes the Aharonov-Bohm resonances.
We also show that the strong renormalization of the tunneling amplitudes that
couple the antidot to the incident edge states, together with the nature of the
Aharonov-Bohm interference process in a chiral system, prevent the occurrence
of perfect resonances as the magnetic field is varied, even at zero
temperature.
