Nonlocality, Self-Adjointness and Theta-Vacuum in Quantum Field Theory in Spaces with Nontrivial Topology

TL;DR

This paper explores how quantum vacuum properties in quantum field theory are affected by nontrivial topology, magnetic vortices, and boundary conditions, revealing nonlocal effects similar to the Aharonov-Bohm phenomenon.

Contribution

It demonstrates the impact of topology and boundary conditions on vacuum quantum numbers in quantum field theory with magnetic vortices, extending understanding of nonlocal quantum effects.

Findings

Vacuum quantum numbers depend on vortex flux

Boundary conditions influence quantum number values

Nonlocal effects analogous to Aharonov-Bohm effect observed

Abstract

We consider an analogue of the Aharonov-Bohm effect in quantum field theory: the fermionic vacuum attains nontrivial quantum numbers in the background of a magnetic vortex even in the case when the spatial region of nonvanishing external field strength is excluded. The dependence of the vacuum quantum numbers on the value of the vortex flux and the choice of the condition on the boundary of the excluded region is determined.