  We study the mutually coupled, strongly interacting bosonic and
non-interacting fermionic, species of unequal masses in the regime were the
retardation effects are an important part of the physics. A cloud of neutral
atoms experiences a synthetic magnetic field because of a vector potential that
imposes a phase shift on the constituents. The magnetic field causes the
oscillations of the magnitude and sign of the effective interaction between
bosons from repulsive to attractive in contrast to the static case. We show
that the dynamics for the gaseous Bose-Fermi mixtures when reaching the
quantum-Hall regime becomes highly nontrivial.
