  We construct a perturbation theory for the SU(2) non-linear Sigma-model in
2+1 dimensions using a polynomial, first-order formulation, where the variables
are a non-Abelian vector field L_mu (the left SU(2) current), and a non-Abelian
pseudovector field $\theta_{\mu}$, which imposes the condition F_{mu nu}(L) =
0. The coordinates on the group do not appear in the Feynman rules, but their
scattering amplitudes are easily related to those of the currents. We show that
all the infinities affecting physical amplitudes at one-loop order can be cured
by normal ordering, presenting the calculation of the full propagator as an
example of an application.
