  We analyze interference phenomena in the quantum-Hall analog of the
Fabry-Perot interferometer, exploring the roles of the Aharonov-Bohm effect,
Coulomb interactions, and fractional statistics on the oscillations of the
resistance as one varies the magnetic field B and/or the voltage V_G applied to
a side gate. Coulomb interactions couple the interfering edge mode to localized
quasiparticle states in the bulk, whose occupation is quantized in integer
values. For the integer quantum Hall effect, if the bulk-edge coupling is
absent, the resistance exhibits an Aharonov-Bohm (AB) periodicity, where the
phase is equal to the number of quanta of magnetic flux enclosed by a specified
interferometer area. When bulk-edge coupling is present, the actual area of the
interferometer oscillates as function of B and V_G, with a combination of a
smooth variation and abrupt jumps due to changes in the number of
quasi-particles in the bulk of the interferometer. This modulates the
Aharonov-Bohm phase and gives rise to additional periodicities in the
resistance. In the limit of strong interactions, the amplitude of the AB
oscillations becomes negligible, and one sees only the new "Coulomb-dominated"
(CD) periodicity. In the limits where either the AB or the CD periodicities
dominate, a color map of resistance will show a series of parallel stripes in
the B-V_G plane, but the two cases show different stripe spacings and slopes of
opposite signs. At intermediate coupling, one sees a superposition of the two
patterns. We discuss the dependence of the interference intensities on
parameters including the temperature and the backscattering strengths of the
individual constrictions. We also discuss how results are modified in a
fractional quantized Hall system, and the extent to which the interferometer
may demonstrate the fractional statistics of the quasiparticles.
