Spin and Isospin

Abstract

Spinor fields can be classified according to the invariants of their derivatives. It is suggested that different invariants describe different interactions of elementary particles. Then the classification of spinor fields becomes a classification of elementary particles and their interactions. A geometric interpretation of isospin is suggested and is used in a model of nucleon interactions. This theory entails an intimate connection between spin and isospin which appears to have some experimental support. Among other things, it connects the pseudoscalar and isospin properties of the pion and accounts for the polarization of the third axis in isospace by the electromagnetic interactions.