Scattering theory for quantum fields with indefinite metric

In this work, we discuss the scattering theory of local, relativistic quant um fields with indefinite metric. Since the results of Haag-Ruelle theory d o not carry over to the case of indefinite metric [4], we propose an axioma tic framework for the construction of in- and out-states, such that the LSZ asymptotic condition can be derived from the assumptions. The central math ematical object for this construction is the collection of mixed vacuum exp ectation Values of local, in- and out-fields, called the "form factor funct ional", which is required to fulfill a Hilbert space structure condition. G iven a scattering matrix with polynomial transfer functions, we then constr uct interpolating, local, relativistic quantum fields with indefinite metri c, which fit into the given scattering framework.