  In this work, we discuss the scattering theory of local, relativistic quantum
fields with indefinite metric. Since the results of Haag--Ruelle theory do not
carry over to the case of indefinite metric, we propose an axiomatic framework
for the construction of in- and out- states, such that the LSZ asymptotic
condition can be derived from the assumptions. The central mathematical object
for this construction is the collection of mixed vacuum expectation values of
local, in- and out- fields, called the ``form factor functional'', which is
required to fulfill a Hilbert space structure condition. Given a scattering
matrix with polynomial transfer functions, we then construct interpolating,
local, relativistic quantum fields with indefinite metric, which fit into the
given scattering framework.
