For instance, in terms of the old properties that are associated with ordinary space-time, all the fermions are identical, whereas it is a fact that there are significant differences between the hyperons, the nucleons, the muons, the electrons, and the neutrinos.
We have previously mentioned some new characteristics currently employed for the classification of particles: the baryon number N and the lepton number / (sometimes referred to as "charges"), the isotopic spin /, and the strangeness S. The baryon number of all the nucleons and hyperons (proton, etc.) is N=+1, and for the antiparticles (antiproton, antineutron, etc.) it is N=-1. In a similar manner, the number / is applied to the leptons (the V and particles have not yet been definitively correlated with it). The N and / numbers may be called together the fermion numbers of the particles. Accordingly, a baryon can transform into light particles only in the presence of an antibaryon, for example p+p ->57t, but the proton cannot decay on its own into pions and positrons. According to our present state of knowledge, N and / are always strictly conserved individually. Some preliminary empirical considerations pointing to nonconservation of the number of baryons have been put forward by Wheeler, in connection with the possible upper limit for stellar masses. We may note here that the nonconservation of the baryon number could be theoretically founded on the description of particles by "anomalous" spinors (Brodskii and Ivanenko), The isospin, on the other hand, is conserved only in the strong interactions, but not in the electro magnetic or weak interactions. Strangeness is also conserved only in the strong interactions. These conservation laws are correlated with invariance with respect to the corresponding transformations in isotopic space, viz. , rotations in the case of isospin conservation, and phase transitions (or gauge transformations) in the case of conservation of the baryon or lepton number. The conservation of ordinary electric charge, i. e. , of current, also follows from phase, or gauge invariance. As a result, the transformation and conservation laws now involve not only ordinary space but also isotopic space, in addition to various phase transformations of the wave function.
The concept of isotopic spin was introduced by Heisenberg, when modern nuclear physics was still in its infancy, in order to describe the family of nucleons. Assuming that the basic nucleon has the isospin its projection 13 may assume the two values and one is made to correspond to the proton = and the other to the neutron = In addition, there are the two antiparticles p and n.
The it meson has the isospin /=1, whose three projections correspond to the three pions (i. e. , two charged and one neutral; thus 13=+1.0, —1). The a+ and it mesons are the antiparticles of each other. In reactions produced by the strong coupling the isospin of the system and the third component are conserved. The isospin of the hyperon is 0, which indicates that there are no other members in the family, though there is still an antiparticle; the isospin of the E hyperons is equal to 1 (a family of three particles, together with three antiparticles); the isospin of the S hyperons is equal to (two components); the isospin of the K mesons is apparently equal to 1/2 (two components, together with their antiparticles).
As we see, the number of possible particles is doubled because of the antiparticles, with the exception of the neutral pions and photons which have no antiparticles (or rather, for which the particles and antiparticles are identical). It has not yet been definitely ascertained whether isospin or a similar concept applies to the leptons; they might possibly form a quadruplet µ ), supplemented by the quadruplet of antiparticles µ+), or perhaps the doublet of muons (µ+, µ ) and their neutrinos v', .7 make a separate set.
As we said before, the kaons and hyperons must be defined by an additional fundamental property, the strangeness, with the particles and antiparticles being assigned a strangeness S of opposite sign (Gell-Mann, Nishijima and Nakano). Strangeness is conserved in strong interactions (for instance, in the coupling between nucleons and pions), and therefore the strange particles produced in the collision of nonstrange particles always appear in pairs, so that their strangeness S, and S2 should cancel out. The conservation of strangeness may be violated when a strange particle decays by weak interaction and transforms into nonstrange particles. There is a fundamental relationship between the ordinary charge Q (in units of e), the third isospin component the baryon number N, and the strange ness S, which holds for all the pions, kaons, and baryons, viz., Q = 13+ S The combination Y = N+S is an important concept, known as the hypercharge.