  In this paper we construct the Lagrangian and Hamiltonian formulations of N=4
supersymmetric systems describing the motion of an isospin particle on a
conformally flat four-manifold with SO(4) isometry carrying the non-Abelian
field of a BPST instanton. The conformal factor can be specified to yield
various particular systems, such as superconformally invariant mechanics as
well as a particle on the four-sphere, the pseudosphere or on R x S^3. The
isospin degrees of freedom arise as bosonic components of an additional
fermionic N=4 supermultiplet, whose other components are rendered auxiliary by
a nonlocal redefinition. Our on-shell component action coincides with the one
recently proposed in arXiv:0912.3289.

High Energy Physics - Theory