On isobaric spin space

Abstract

The previously proposed treatment of reflexions as special cases of continous transformations is developed in detail by a method based on the introduction of 3-dimensional structures (triads). The requirement of Lorentz invariance of the definitions of an unreflected and a fully reflected state of a triad can be fulfilled only if from a relativistic point of view a triad has axial symmetry only. Rotations round the symmetry axis are Lorentz invariant processes. The development of the formalism leads to the introduction of a 4-dimensional space with (nearly) Euclidean properties. All its operations find interpretations in terms of local structures in physical space. Lorentz invariant operators are found which have exactly the properties of isospin operators and thus lead to an interpretation of isospace. One of its main characteristics is its axial symmetry which can be extended to spherical symmetry in a limited way only. The well known cases arise; they have only one common Lorentz invariant operator, corresponding to the electric charge operator.