Non‐Relativistic Limit of Dirac Hamiltonians With Aharonov–Bohm Fields

ABSTRACT We characterize the families of self‐adjoint Dirac and Schrödinger operators with Aharonov–Bohm magnetic field, and we exploit the non‐relativistic limit of infinite light speed to connect the former to the latter. The limit consists of the customary removal of the rest energy and of a suitable scaling, with the light speed, of the short‐scale boundary condition of self‐adjointness. This ensures that the scattering length of the Aharonov–Bohm interaction is preserved along the limit. Noteworthy is the fact that the whole family of Dirac‐AB operators is mapped, in the non‐relativistic limit, into the physically relevant sub‐family of ‐wave, angular‐momentum‐commuting, Schrödinger–AB Hamiltonians with relativistic Dirac approximants.