The family of leptons e , e+, v, v, v , 7 is headed by the photon y, i. e. , the electromagnetic field. We will add to the table the gravitational field (denoted by g) as well, even though, as we said, gravitational waves and their corresponding field quanta (gravitons) have not yet been discovered. In any case, the gravitational field, being associated with the curvature of space-time, must be taken into account in the description of physical reality, and its transverse part, which can take the form of radiation, ought to be in many ways equivalent to ordinary matter. It is predicted that the graviton will have no rest mass and that its spin will be S=2 (units of h/2n).
After having segregated all the known particles into groups in accordance with the classification of Gell-Mann and Nishijima and Nakano, with the addi tion of the leptons, photons, gravitons, and the newly discovered resonons, it would be natural to seek a theoretical foundation for this grouping. The first successful attempt was made in the beginning of 1956 by d'Espagnat and Prentki, who took as a basis a three-dimensional isospace and considered in it not only rotations, which lead to isospin, but also reflections; by means of the latter it was possible to explain strangeness. This procedure describes particles by defining their isotopic properties; it is thus assumed that the three n mesons form a pseudovector in isospace (isobosons), as do the three E hyperons, the two nucleons (the proton and neutron) and the K mesons form in isospace spinors of the first kind (isofermions), and the cascade FL hyperons form spinors of the second kind (anti-isofermions), differing from the former only under inversions (by the sign) but not under rotations or Lorentz transformations. (Spinors are wave functions of the Dirac type, describing the particles of spin they may be said to be half vectors, or square roots of vectors, that is to say, tensors of rank . ) The correct value for the hypercharge of every particle is then obtained by subtracting the anti-isofermion number from the isofermion number.
It has been predicted by Gell-Mann that in principle particles with S=3 may exist. However, the d'Espagnat-Prentki theory does not allow for a strangeness larger than 2, and this is for the time being in full agreement with experimental data.
The discovery of the new particle properties, isospin, strangeness, and the baryon and lepton numbers, and the resultant classification of particles, made in 1955-1956, have been major advances in particle physics. To
those should be added the very recent discovery of the groups of "resonons", the second type of neutrinos, and the neutral anti-E particle.
We should pause to consider briefly the further development of this problem, however, in order to appraise the shortcomings in the system of Nishijima, Gell-Mann, and d'Espagnat-Prentki and to outline the prospects that look most promising in this particular field.
The inadequacy of the given system is clearly exhibited by two facts. First, it does not take into account the leptons and photons and it leaves out gravitation altogether. Second, the systematization does not account for the similarity displayed by all the baryons in their interactions with is and K mesons. All the independent coupling constants of the nucleons and hyperons with IT and K mesons have been empirically shown to be virtually the same, in fact. As a result, a number of more general theories have been produced.
In some of the theories the three-dimensional isospace is generalized to a four-dimensional space, mostly taken to be Euclidean (Salam, Polkinghorne, Schwinger, etc.). Some authors, however, use pseudo-Euclidean space. Four-dimensional isospace provides a more unified treatment of particles. Thus, for instance, the A and the three E hyperons are characterized by a single four-dimensional isotopic pseudovector; it then becomes clear that the coupling constants of the A and E hyperons with pions are actually identical, and not independent as in the earlier three-dimensional system. Schwinger's system classifies not only the mesons and baryons, but also the leptons; thus e_, v, form an isotriplet; the photon proves to be a member of a new triplet family, whose other two charged components are not yet known, but are only theoretically predicted.
Schwinger's theory also predicts a fourth a meson (a similar particle, alternatively called a p, a, or le" meson, was predicted in a number of papers by A. M. Baldin and some others). This particle has still not been discovered either. Several "intermediate" heavy bosons have been also variously proposed, as the p; rticle mediating between the baryons and leptons.