A Theory of the Fundamental Interactions

This note is an account of some developments in an effort to find a description of the present stock of elementary particles within the framework of the theory of quantized fields’. The theory of fields suggests that the spin values of $5 for F(ermi)-D(irac) fields, and of 0 and 1 for B(ose)-E(instein) fields are not only exceptional in their simplicity but. are likely to be unique in the possibility of constructing a consistent formalism for particles with mass and electric charge. We shall attempt to describe the massive, strongly interacting particles by means of fields with the smallest spin appropriate to the statistics, O(B.E.) and s(F.D.). Spin 1 remains a possibility for B.E. fields but will be assumed to refer to a different family of particles, of which the electromagnetic field may be a special example. If the spin values are thus limited, the origin of the diversity of known particles must be sought in internal degrees of freedom. We suppose that the various intrinsic degrees of freedom are dynamically exhibited by specific interactions, each with its characteristic symmetry properties, and that the final effect of interactions with successively lower symmetry’ is to produce a spectrum of physically distinct particles from initially degenerate states. Thus we attempt to relate the observed masses to the same couplings responsible for the production and interaction of these particles The general multicomponent Hermitian field x separates into the F.D. field J/ and the B.E. field 4. The representation of spin $5 requires 4 components, while spin 0 demands 5 components, decomposable into a scalar and a vector. The existence of internal degrees of freedom is expressed by an additional multiplicity