Self-Adjointness and Polarization of the Fermionic Vacuum in the Background of Nontrivial Topology

TL;DR

This paper investigates how a singular magnetic string influences the fermionic vacuum in a 2D setting, analyzing the effects of boundary conditions and magnetic flux on vacuum polarization and quantum numbers.

Contribution

It introduces the most general boundary conditions compatible with self-adjointness for the Dirac Hamiltonian in a magnetic string background, exploring their impact on vacuum polarization.

Findings

Vacuum polarization depends on boundary conditions and magnetic flux.

Self-adjoint extension parameters influence induced quantum numbers.

The study provides a comprehensive framework for analyzing fermionic vacuum in topologically nontrivial backgrounds.

Abstract

Singular configuration of an external static magnetic field in the form of a string polarizes vacuum in the secondly quantized theory on a plane which is orthogonal to the string axis. We consider the most general boundary conditions at the punctured singular point, which are compatible with the self-adjointness of the two-dimensional Dirac Hamiltonian. The dependence of the induced vacuum quantum numbers on the self-adjoint extension parameter and the flux of the string is determined.