Effects of singular external fields and boundary condition on the vacuum of massless fermions in QFT

TL;DR

This paper investigates how singular external magnetic fields and boundary conditions influence the vacuum state of massless fermions in quantum field theory, emphasizing the role of self-adjoint boundary conditions at singular points.

Contribution

It introduces the most general boundary conditions that ensure self-adjointness of the Dirac Hamiltonian in the presence of a singular vortex magnetic field.

Findings

Boundary conditions significantly affect the vacuum structure.

Self-adjoint extensions are characterized for the Dirac Hamiltonian.

The study provides a framework for analyzing fermionic vacuum in singular magnetic fields.

Abstract

Effects of the configuration of an external static magnetic field in the form of a singular vortex on the vacuum of a quantized massless spinor field are studied. The most general boundary conditions at the punctured singular point which make the twodimensional Dirac Hamiltonian to be self-adjoint are employed.