Fermions in the background pseudopaticle field in an O(5) formulation

The eigenvalue equation for a fermion in the field of the pseudoparticle of the Yang-Mills theory is solved using the formalism of the four dimensional hypersphere. All the fermionic zero modes for a SU(2) gauge group belong to a singly nondegenerate O(5) representation. In the case of isospin n their multiplicity is given by 2n(n+1)(2n+1)/3. If the fermions are in the adjoint representation the eigenfunctions of the zero modes are directly obtainable from considerations pertaining to the supersymmetry of the Yang-Mills Lagrangian. (Auth.)