Relativistic corrections of order $m{\alpha }^6$: singular operators and regularization

The finite operators are derived for the nonrecoil (leading order in the $(m\mathrm{/}M)$ expansion) relativistic corrections in hydrogen-like atoms and ions at orders $m{\alpha }^6$ in the two- and three-body formalism beyond the adiabatic approximation. Singular operators that appear in the derivation are analysed, and various regularization methods are discussed.