Quantum Numbers of the Theta Vacuum in (2+1)-Dimensional Spinor Electrodynamics: Charge and Magnetic Flux

TL;DR

This paper investigates how a magnetic string influences the vacuum quantum numbers in (2+1)-dimensional spinor electrodynamics, analyzing boundary conditions, flux dependence, and representation choices to understand the quantum effects of topological configurations.

Contribution

It provides a comprehensive analysis of vacuum polarization effects and quantum numbers induced by magnetic strings in (2+1)D spinor electrodynamics, considering self-adjoint boundary conditions and representation dependence.

Findings

Vacuum quantum numbers depend on boundary conditions and string flux.

Self-adjoint extension parameters influence induced charge and flux.

Representation choice affects the quantum number calculations.

Abstract

A singular configuration of an external static vector field in the form of a magnetic string polarizes the vacuum of a second-quantized theory on the plane orthogonal to the string axis. The most general boundary conditions at the punctured singular point that are compatible with the self-adjointness of two-dimensional Dirac Hamiltonian are considered. The dependences of the induced vacuum quantum numbers on the parameter of the self-adjoint extension, on the string flux, and on the choice of irreducible representation of the matrices in (2+1)-dimensional spacetime are disscussed.