  We compare two different methods of computing form factors. One is the well
established procedure of solving the form factor consistency equations and the
other is to represent the field content as well as the particle creation
operators in terms of fermionic Fock operators. We compute the corresponding
matrix elements for the complex free fermion and the Federbush model. The
matrix elements only satisfy the form factor consistency equations involving
anyonic factors of local commutativity when the corresponding operators are
local. We carry out the ultraviolet limit, analyze the momentum space cluster
properties and demonstrate how the Federbush model can be obtained from the
$SU(3)_3$-homogeneous sine-Gordon model. We propose a new class of Lagrangians
which constitute a generalization of the Federbush model in a Lie algebraic
fashion. For these models we evaluate the associated scattering matrices from
first principles, which can alternatively also be obtained in a certain limit
of the homogeneous sine-Gordon models.
