What happens to wavepackets of fermions when scattered by the Maldacena-Ludwig wall?

Abstract

We study wavepackets of exotic excitations after two-dimensional fermions are scattered by the boundary condition constructed by Maldacena and Ludwig, which turns elementary excitations into exotic fractionally-charged objects. They are of interest in the s-wave approximation of the fermion-monopole scattering in four-dimensional QED and of the multi-channel Kondo effect. We in particular give an explicit expression of the outgoing state of a pair of such particles; we then examine its properties, such as the charge density $⟨J(x)⟩$ and the expectation value $⟨N⟩$ of the number of fermions and anti-fermions in the state. The charge density $⟨J(x)⟩$ is found to be localized with its integral finite and fractional, while the expectation value $⟨N⟩$ diverges when the wavepacket is localized to a point.

19 pages + appendices, 4 figures