  The Jackiw-Pi model in 2+1 dimensions is a non-relativistic conformal field
theory of charged particles with point-like self-interaction. For specific
values of the interaction strengths the classical theory possesses vortex and
multi-vortex solutions, which are all degenerate in energy. We compute the full
set of first-order perturbative quantum corrections. Only the coupling constant
g^2 requires renormalization; the fields and electric charge e are not
renormalized. It is shown that in general the conformal symmetries are broken
by an anomalous contribution to the conservation law, proportional to the
beta-function. However, the beta-function vanishes upon restricting the
coupling constants to values g^2 = +/- e^2, which includes the case in which
vortex solutions exist. Therefore the existence of vortices also guarantees the
preservation of the conformal symmetries.
