  Differential regularization is applied to a field theory of a
non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$
self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons
gauge field. Renormalized configuration-space amplitudes for all diagrams
contributing to the $\phi {}^{*} \phi {}^{*} \phi \phi$ 4-point function, which
is the only primitively divergent Green's function, are obtained up to 3-loop
order. The renormalization group equations are explicitly checked, and the
scheme dependence of the $\beta$-function is investigated. If the
renormalization scheme is fixed to agree with a previous 1-loop calculation,
the 2- and 3-loop contributions to $\beta(\lambda,e)$ vanish, and
$\beta(\lambda,e)$ itself vanishes when the ``self-dual'' condition relating
$\lambda$ to the gauge coupling $e$ is imposed.
