Towards Unified and Convergent Theory of Elementary Particles

Abstract

In order to get rid of the well-known divergence difficulty in the quantum field theory, fictitious particles with an indefinite metric are introduced. The difficulty concerning the probabilistic interpretation caused by the indefinite metric is satisfactorily avoided by making use of the of fictitious particles, characterized by the complex poles. Based on such a general possibility, we investigate the Nagoya model assuming B-matter to be a unified assembly of fictitious particles. The divergence difficulty in the quantum field theory has been a long-pending object for the theoretical physicists from its beginning and many efforts to overcome this difficulty have been made without any satisfactory solution. Among these attempts, however, the introduction of the indefinite metric in the Hilbert space seems to have a special theoretical ground/) when taking into consideration the recent investigation of the axiomatic formulation of the quantum field theory.2) As noticed by many authors, this attempt seems still to have a serious difficulty that it can not reconcile with the probabilistic interpretation in the quantum theory or with the requirement of the macroscopic causality.3),4) However, it should be noticed that the latter conclusion is based on a purely perturbational consideration. Let us consider the well-known Pauli-Villars type regularization. Fictitious particles introduced to regularize the divergence have in general a large mass and interact with physical particles. Thus, at high energies over the threshold of the production of these fictitious particles, they must come out with an indefinite metric and thus violate the probabilistic interpretation. 4 ),O) Is this consideration, however, really correct? There necessarily arises the question of the stability of these particles. Such a fictitious particle which has a large mass and interacts with physical particles in general must not be stable. However, it should be noticed that the instability of fictitious particles with indefinite metric is only superficial and has an essentially different aspect from the instability of the usual unstable particles with a definite metric. That 1S,