(Received November 16, 1970)
Starting with the system of particles with the same common mass but with various different spins, we make the masses split based on the tadpole interaction. In this way all the defects of the theory of infinite multiples are remedied.
This short paper develops an idea proposed, in the boson case, by the present author in a previous paper (hereafter referred to as I). Since we have treated a boson case in I, so we will treat a fermion case here. As was mentioned in I, the defects of the theory of infinite multiplets, namely the existence of space-like solutions, the violation of CPT invariance, the violation of the relation between spin and statistics and especially the well-known no-go theorem, have rejected the usual method of quantization based on the canonical formalism. The author has proposed the following idea: First one treats the case in which all the particles have the same common mass but different various spins, and next introducting a new scalar particle Q, one makes the masses of the particles split with respect to the spins. Along this line of thought we can evade all the defects. An example of the boson case is easily obtained. See Ref. 1) in this context.
URL : http://ptp.ipap.jp/link?PTP/46/659/
DOI : 10.1143/PTP.46.659