Local duality, chiral supersymmetry and fermion-like formulation of non-Abelian pure gauge fields

This work generalizes the fermion-like formulation of the Maxwell theory to the non-Abelian Yang–Mills theory without matter fields. This is a new representation of the Lie algebra valued electric and magnetic fields. The resulting equations of motion are invariant under the chiral transformation. In this formulation, duality is a kind of chirality. We may also define local duality transformations in terms of space-time dependent parameters. There is an N=1 supersymmetry for the Dirac-like operator in this representation. Received: 19 June 2000 / Revised version: 10 October 2000 / Published online: 15 March 2001