  We study the Lagrangian for a sigma model based on the non-compact Heisenberg
group. A unique feature of this model -- unlike the case for compact Lie groups
-- is that the definition of the Lagrangian has to be regulated since the trace
over the Heisenberg group is otherwise divergent. The resulting theory is a
real Lagrangian with a quartic interaction term. After a few non-trivial
transformations, the Lagrangian is shown to be equivalent -- at the classical
level -- to a complex cubic Lagrangian. A one loop computation shows that the
quartic and cubic Lagrangians are equivalent at the quantum level as well. The
complex Lagrangian is known to classically equivalent to the SU(2) sigma model,
with the equivalence breaking down at the quantum level. An explanation of this
well known results emerges from the properties of the Heisenberg sigma model.
