PARTICLE CLASSIFICATION. ATTEMPTS TO CREATE A UNIFIED THEORY OF MATTER Let us construct a table of elementary particles (including the resonons), arranging them essentially by order of increasing mass (simi larly to the way Mendeleev arranged the chemical elements by order of increasing atomic weight), and then segregate them into families, in accordance with current views. The mass or self-energy of a particle is ultimately its most significant characteristic, as it is for a nucleus and an atom, as well as a planet or a star.
Let us now pause to examine the fundamental, irreducible properties of particles that are known. An important property after the mass is the spin of the particle, i. e. , its intrinsic angular momentum. In terms of spin the particles fall into two distinct categories: the fermions, which have half-integral spin and are subject to Pauli's exclusion principle and to Fermi statistics, and the bosons, which have integral spin and obey the Bose statistics. The spin of a particle defines also the number of components of the corresponding wave function. Thus, for instance, in the case of a photon (spin S=1, in units of h/2,c) we have a vector wave function with three independent components; for the graviton (S = 2) we have a wave function in the form of a symmetric tensor of the second rank (10 components, 5 of them independent); for the it and K mesons (S = 0) we have a single component wave function; finally, for all the fermions (S= the wave function will be a spinor (of the Cartan type, or a tensor of rank one-half), in the general case with four components (Dirac-type bispinor); only in the case of the electron-type neutrinos v and, apparently, the other, muon type neutrinos v', is it sufficient to take a 2-component spinor (of the Weyl type). It is further necessary to take into account the parity of the wave function, defined by the behavior of the function under a mirror reflection of the coordinates, or respectively under a time reversal. The wave function of the it and K mesons then turns out to be a pseudoscalar and not a scalar (also characterized by a single component). A scalar and a pseudoscalar behave in the same way under all continuous transformations of the coordinates (and of time), such as rotation and Lorentz transforma tions, but under mirror reflections a pseudoscalar changes sign, whereas a scalar remains invariant.
Up to this point we have been discussing the "old" properties of particles and their behavior in space-time. The fundamental characteristics of space-time determine the invariance properties and the principal con servation laws, viz., 1) the homogeneity of space leads to the invariance of the field equations (and the corresponding Lagrangians) with respect to translations, and to the law of conservation of momentum; 2) the homo geneity of the time dimension leads to the law of conservation of energy; and 3) the isotropy of space leads to the invariance with respect to rotation and to the conservation of angular momentum.
The transformations of 3- and 4-dimensional translations and rotations and the corresponding conservation laws have been known for a long time; invariance with respect to mirror reflections of the coordinates (i. e. , the equivalence of left and right) and with respect to time reversal was also well-known, but the corresponding laws of conservation of the "parity" of the wave function were developed, of course, only after quantum mechanics had come into being, in 1924-1927. In the middle of the fifties it was found (thanks to the work of Lee, Yang, Wu, and others), however, that space parity (P) is conserved only in the strong, but not in the weak, interactions. What is conserved at all times is a composite quantity, the "combined parity", equal to the product of P and the charge parity C. Without going into detail, we may describe the basic operation involved not as a simple transition into the mirror world (since in fact mirror symmetry does not always hold), but rather as such a transition coupled with a change of sign of the charges (i. e. , together with charge conjugation, or particle-anti particle conjugation). We can see, therefore, that it is impossible to remain within the framework of ordinary 4-dimensional space-time with the corresponding conservation laws, and that it is necessary to appeal to new particle properties and new conservation laws in order to understand the phenomena involved. The resultant new quantum numbers provide a means of classifying the particles more accurately than can be done in terms of spin and parity alone.