On a Convergent Model of Quantum Field Theory with Indefinite Metric

A convergent model of quantum field theory with indefinite metric is proposed to the case of an indirect interaction between a physical neutnd scalar field and a physical spinor field, by introducing four kinds of unphysical spinor fidcls which play the roles of the in termediate states connecting these two of physical fielcl~. Two of these unphysical fields are set to have negative anticommutators and consequently this fact makes the metric of our Hilbert space indefinite; nevertheless it is shown that the unitarity of the actual S-matrix holcls strictly. Final results are such that every vertex in the usual local theory is exactly replaced with some kind of extended vertex in this model which prepares the sufficient convergency for all results. Although the extended vertex in this model becomes singular at the two momentum values depending on the masses of unphysical fields and the coupling constant, it is also shown that there remains a considerable wide degree of freedom to control the stable mass levels of the physical particles as suitably as possible. The definite results about this problem are left for the future.