Spinor analysis of Yang-Mills theory

Abstract

We formulate the Euclidean Yang-Mills gauge theory for isospin in terms of multispinors of SU(2) × SU(2)[= O(4)] × SU(2). The Dirac equation for fermions with arbitrary isospin interacting with the self-dual, conformally covariant Yang-Mills field is analyzed and completely solved for the isovector case. The relevance for this problem of the Atiyah-Singer index theory and its relation to the anomalous divergence of the axial-vector current are also explained.