The scattering of fermions by an infinitely thin flux tube is governed by a Dirac Hamiltonian that requires specification of a one-parameter self-adjoint extension. This Aharonov-Bohm scenario arises generically for cosmic strings. In particular for some range of the extension parameter the string can bind fermions.

• Received 8 November 1988

DOI:https://doi.org/10.1103/PhysRevD.40.1346