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Self-adjointness of the Dirac Hamiltonian in point instanton and meron fields

The instanton and meron field configurations have been used extensively in the literature. They are used in solitonic solutions arising from gravitation to attempts at explaining the confinement of quarks in QCD. We examine the Dirac Hamiltonian in the field of the point Yang-Mills and CP/sub 1/ instantons as well as the meron configurations to determine whether there is a self-adjointness problem. We find that both CP/sub 1/ and the Yang-Mills instanton Hamiltonians are indeed self-adjoint but that the meron solution admits a U(2) worth of self-adjoint extensions. These extensions will show up in all calculations involving meron-fermion couplings and possibly also in characterizing the SU(2) vacuum structure.