Isospin und Parität in der nichtlinearen Spinortheorie

Abstract

The isospin transformation properties and the space reflection symmetry in a nonlinear field theory of elementary particles, as proposed by HEISENBERG and coworkers, are studied. In section I it is shown that the nonlinear equation for a 4-component spinor operator ψ is equivalent to the equation for a 4-component WEYL- isospinor operator χ. In this WEYL representation of the theory the PAULI-GÜRSEY transformations and the TOUSCHEK transformation can be replaced by the conventional forms of the isospin rotations and the gauge transformation of the first kind, respectively. In section II an attempt is made to introduce parity in a rigorous manner using the invariance of the equation under l-Inversion l→ —l. Some important aspects of symmetry operations which involve transformations of parameters, are discussed. By virtue of the parity symmetry a DIRAC notation may be introduced, and the nonlinear equation then corresponds to a TOUSCHEK invariant equation of the DIRAC type with nonlinear vector- and axialvector terms of equal strength. The existence of particles with finite mass suggests a degeneracy of the ground state “world” with respect to parity. In section III and IV the TAMM—DANcoFF-method is applied for an estimate of the masses of nucleons and bosons with spin and isospin zero or one, using the simpler WEYL representation with and without consideration of the parity symmetry, respectively.