The new bosons have also been predicted by the "compensating field" theory recently developed by Yang and Mills and by Sakurai, a theory held by many physicists (Schwinger, Utiyama, Gell-Mann, Feynman, etc.). This theory once again stresses the point that to each conservation law there corresponds some field—for instance, to the conservation of electric charge there corresponds the electromagnetic field and its quanta, the photons. Ana logously to the conservation of baryon charge, of isotopic spin, and of strangeness there must correspond three new types of particles.
These ideas were applied by A.M. Brodskii, G.A. Sokolik and by us to a new treatment of gravitation. It is possible that part of the boson-type vector resonons R. are the same as the vector mesons predicted by the "compensating field" theory.
It has been suggested that isotopic and ordinary space might be closely related and that transitions might be possible from one to the other (Ivanenko-Brodskii and G.A. Sokolik, Schwinger, Pais, Vigier, Yukawa); a total reflection could be then defined, as the product of reflections in ordinary and in isotopic space. If one allows for the possibility of transitions from ordinary into isospace, this means that isotopic properties could go over into ordinary "external" properties. Roughly speaking, if such a hypothesis should prove correct, a particle, for instance, would be able to lose its isospin and acquire ordinary spin instead. The compensating field theory, which assumes that the phase transitions in isospace are dependent on the ordinary coordinates, also runs along similar lines.
In this connection, Schwinger noted an interesting regularity which applies to neutral bosons: the K mesons do not have ordinary spin, but have an isospin and strangeness; the photons have both ordinary spin and isospin (within Schwinger's scheme); finally, the gravitons should possess spin but no isotopic properties at all. It has been proposed by De Broglie and Vigier that isospace may be considered as an extension of ordinary space inside the particles.
Aside from the 03 group of rotations in three-dimensional isospace, use has also been made of the groups O, (Salam and Polkinghorne), 03 (Behrends, Fronsdal), 07 (Tiomno), and even 08 (rotations in eight-dimensional isospace, Gourski). Out of various other symmetry groups (almost all of which are compact Lie groups, i. e. , continuous and described by unitary
matrices), theoreticians have recently found particular interest in the groups (the group of 3X3 unimodular unitary matrices) and G2 (the anomalous Cartan group which gives a regular representation of the multiplet components in 14 dimensions). However none of the groups has yet provided a complete classification of the particles and resonons into families. We thus see that in spite of extensive research the problem is far from being solved.
In his summary review of the group-theoretical approach recently presented at the Eleventh International Conference on High-Energy Physics (elementary particles) held in Geneva in the summer of 1962, d'Espagnat expressed particular hopes for the SU3 and G2 group treatment, though he also did not consider the problem solved as yet.
A possible method of classification of particles has been proposed, on the basis of which particles of spin '/2 (fermions) are associated with a class of spinors that differ only in the way they behave under space or time reflections.
Somewhat earlier Yang and Tiomno proposed using in the same way the recip rocal cofactors 1, —1, +i, —i, to differentiate between types of mirror-image spinors (classes A, B, C, D), and to assc. fate with them the electrons, neutrinos and µ mesons, respectively. ?I. Mirianashvili and Gyurshi suggested using in the coalescence method combinations of spinors of different classes, for example A and D, rather than spinors of one class as was done before; unusual boson functions are then obtained, which could perhaps be correlated with the K mesons. A. M. Brodskii, in conjunction with G. A. Sokolik and us, extended these considerations to include a supplementary matrix factor for inversions; in that case, if a spinor behaves normally under space reflections, but under a time reflection its wave function is additionally multiplied by ys, then this spinor will show an "anomalous" behavior in some relations. It then becomes possible to associate the anomalous spinors with the strange fermions. According to such an interpretation, developed in part by Salam, Taylor, Ognevetskii, and Chou Kuang-chao, the origin of the "strange" properties may be rooted in the anomaly of the spinors, i. e. , the way in which their behavior differs under space and time reflections.