Zur Theorie der Elementarteilchen

Abstract

The equation ${\gamma_{\nu}}\frac{\partial}{{\partial{x_{\nu}}}}\psi\pm{l^2}{\gamma_{\mu}}{\gamma_5}\psi\left({\bar{\psi}{\gamma_{\mu}}{\gamma_5}\psi}\right)=0$ is analysed with respect to the following consequences. In I the group theoretical structure of the equation is studied. The equation is invariant under a number of continous transformations: the inhomogeneous Lorentzgroup, the transformations of Pauli, Gürsey and Touschek, and the scale transformation [x → η x orψ → η ^3/2 ψ (x η, l η)]. The Pauli-Gürsey group is used for the interpretation of the isospin; the γ ₃-transformation of Touschek establishes a quantum number I _N, and the scale transformation leads to a quantum number l _N, which both are connected with the baryonic and the leptonic number. The strangeness s = l _N - l _Q is suggested to be connected with the discrete groups of the equation and could then be defined and conserved only modulo 4. Of the discrete groups only the well known transformations P, C and T and the reversal of l(l → - l) are briefly discussed. In II the vacuum expectation values of products of two field operators are studied. These values are considered to be only in a first approximation invariant under the Isospin-group. The deviations from the Pauli-Gürsey symmetry in higher approximations are supposed to be due to the replacement of the state “vacuum” by an idealised state “world”, which possesses an infinite isospin; the strange particles are consequently interpreted as states which “borrow” an isospin 1/2 or 1 from the ground state “world”. The concept of “One particle-wavefunctions” is discussed in III. The fermions of finite mass belong to wavefunctions obeying a Klein-Gordon-spinor equation instead of a Dirac equation. The connection with the conventional formalism of the Dirac equation is treated in detail. The process of ^-conjugation springing from these discussions is used for a variation of the methods of approximation needed later on for the determination of mass values and the pion-nucleon coupling constant.

Der Aufenthalt von K. Yamazaki in Göttingen und München wurde durch die Alexander v. Humboldt-Stiftung ermöglicht.