Monopole-fermion scattering and varying Fock space

TL;DR

This paper offers a four-dimensional interpretation of monopole-fermion scattering, revealing how the Fock space of fermions depends on monopole degrees of freedom and changes during scattering, providing new insights into fractional fermion numbers.

Contribution

It extends the fermion-rotor system to four dimensions, showing how the outgoing state resides in a different Fock space, advancing understanding of monopole-fermion interactions.

Findings

Fock space depends on monopole rotor degrees of freedom.

Scattering induces a change in the fermionic Fock space.

Outgoing states have fractional fermion numbers.

Abstract

We propose a four-dimensional interpretation of the outgoing state of the scattering of a massless fermion off a Dirac monopole. It has been known that such a state has fractional fermion numbers and is necessarily outside the Fock space on top of ordinary perturbative vacuum, when more than two flavours of charged Dirac fermions are considered. In this paper, we point out that the Fock space of the fermions depends on the rotor degree of freedom of the monopole and changes by a monopole-fermion s-wave scattering. By uplifting the fermion-rotor system introduced by Polchinski, from two to four dimensions, we argue that the outgoing state can be understood as a state in a different Fock space.