Nonlocality effects on fermions confined within a hard-wall potential

Abstract

We investigate nonlocality effects on the energy spectrum of spin-$1/2$ fermions confined by hard-wall potentials. Starting from a nonlocal Dirac theory with a modified kinetic term, we formulate the associated field equation in flat spacetime using cylindrical coordinates. By exploiting the eigenvalue spectrum of the squared Dirac operator, the original infinite-order equation is reduced to a finite-order problem. We also show that on the branch continuously connected to the local Dirac theory the nonlocal corrections can be encoded in an effective fermion mass. We then find analytical energy spectra for two confining geometries: a cylindrical hard wall and a quantum ring defined by two concentric cylindrical boundaries. In both cases, the radial equations reduce to Bessel equations and the boundary conditions quantize the allowed modes. The local hard-wall spectra are recovered for $Λ\to\infty$, whereas finite nonlocality shifts the mass contribution and, consequently, the particle--antiparticle energy separation. These results provide a direct characterization of nonlocal effects in quantum-confined fermionic systems.