Spin polarisation by external magnetic fields, Aharonov-Bohm flux strings, and chiral symmetry breaking in QED$_3$

TL;DR

This paper calculates vacuum spin induced by Aharonov-Bohm flux strings in massless QED3, explores chiral symmetry breaking under magnetic fields, and discusses related vacuum polarization effects in various QED models.

Contribution

It provides explicit computations of induced vacuum spin in QED3, confirms the role of flux in observable quantum numbers, and relates chiral symmetry breaking to induced spin phenomena.

Findings

Vacuum spin around flux strings matches index theorem predictions.

Induced quantum numbers are non-periodic in flux, making flux strings observable.

Chiral symmetry breaking is connected to induced spin in QED3.

Abstract

In the first part, the induced vacuum spin around an Aharonov-Bohm flux string in massless three-dimensional QED is computed explicitly and the result is shown to agree with a general index theorem. A previous observation in the literature, that the presence of induced vacuum quantum numbers which are not periodic in the flux make an integral-flux AB string visible, is reinforced. In the second part, a recent discussion of chiral symmetry breaking by external magnetic fields in parity invariant QED$_3$ and its relation to the induced spin in parity non-invariant QED$_3$ is further elaborated. Finally other vacuum polarisation effects around flux tubes in different variants of QED, in three and four dimensions are mentioned.