Vacuum polarisation around an Aharonov-Bohm solenoid

Abstract

The quantisation of a charged scalar field in an externally specified electromagnetic field, described by the vector potential A_i = ∂_iƒ with ƒ(t,r,θ,z)=Bθ is discussed. The electromagnetic field is zero everywhere except at the origin; a singular magnetic field (Aharonov-Bohm field) exists at the origin. The vacuum polarization around such a magnetic field is computed and the non-local behaviour is discussed.