(Received December 17, 1956)
It is shown that the theory of d'Espagnat and Prentki (henceforth referred to as DP) on a mathematical formulation of the Gell-Mann-Nishijima scheme can be generalized so as to accomodate particles of higher isofermion number. Modifications made for this purpose are: (i) the isospinor formalism is adopted for all kinds of particles instead of DP's isospinor-isotensor mixed formalism; and (ii) the invariance under inversion of isobaric spin space, imposed by DP as a postulate on strong and electromagnetic interactions, is replaced by the invariance under a continuous phase transformation group GU generated by the operator U representing isofermion number. These modifications lead not only to extension of the fremework but also to refinement of the theory as follows. In our formalism, (a) the transformation properties of field viriables with respect to GU are unambiguously determined without resort to the assumption, made by DP, that only the Yukawa interactions appear in the interaction Lagrangian; (b) the isofermion number U proves to be the number of suffices of the first kind minus that the second kind, with respect to inversion, of the isospinor describing a particle; and (c) DP's identity Q = I3 + ½ U among the electric charge Q, the third component of is obaric spin I3, and U as well as Racah's identity P = exp (i½ π U) between U and the isobaric parity P follows directly from an identical relation among the transformation groups concerned.
URL : http://ptp.ipap.jp/link?PTP/17/592/
DOI : 10.1143/PTP.17.592