The SU(2) instanton and the adiabatic evolution of two Kramers doublets

The adiabatic evolution of two doubly degenerate (Kramers) levels is considered. The general five-parameter Hamiltonian describing the system is obtained and is shown to be equivalent to one used in the Jahn - Teller system. It is shown explicitly that the resulting SU(2) non-Abelian geometric vector potential is that of the ( SO(5) symmetric) SU(2) instanton. Various forms of the potentials are discussed.