Fermionic condensate in a conical space with a circular boundary and magnetic flux

TL;DR

This paper analyzes the behavior of fermionic condensates in a conical spacetime with a circular boundary and magnetic flux, revealing how boundary conditions and magnetic flux influence the condensate's properties.

Contribution

It provides new integral representations for the fermionic condensate in conical geometries with magnetic flux and boundary conditions, including special cases at the cone apex.

Findings

Fermionic condensate is a periodic function of magnetic flux with flux quantum period.

At large distances, the condensate decays exponentially depending on the cone's opening angle.

For non-half-integer flux ratios, the boundary-free condensate vanishes for massless fields.

Abstract

The fermionic condensate is investigated in a (2+1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. It is assumed that on the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The fermionic condensate is a periodic function of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the fermionic condensate is decomposed into boundary-free and boundary-induced parts. Two integral representations are given for the boundary-free part for arbitrary values of the opening angle of the cone and magnetic flux. At distances from the boundary larger than the Compton wavelength of the fermion particle, the condensate decays exponentially with the decay rate depending on the opening angle of the cone. If the ratio of the magnetic flux to the flux quantum is not a half-integer number, for a massless field the boundary-free part in the fermionic condensate vanishes, whereas the boundary-induced part is negative. For half-integer values of the ratio of the magnetic flux to the flux quantum, the irregular mode gives non-zero contribution to the fermionic condensate in the boundary-free conical space.