We present a general analysis of the effective potential for neutrino propa
gation in matter, assuming a generic set of Lorentz invariant non-derivativ
e interactions. We find that in addition to the known vector and axial vect
or terms, in a polarized medium also tensor interactions can play an import
ant role. We compute the effective potential arising from a tensor interact
ion. We show that the components of the tensor potential transverse to the
direction of the neutrino propagation can induce a neutrino spin flip, simi
lar to the one induced by a transverse magnetic field. [S0556-3821(99)00219
-2].