We investigate the self-adjoint extensions of the Dirac operator of a massive one-dimensional
field of mass m confined in a finite filament of length L. We compute the spectrum of vacuum
fluctuations of the Dirac field under the most general dispersionless boundary conditions. We identify
its edge states in the mass gap within a set of values of the boundary parameters, and compute the Casimir energy of the discrete normal modes. Two limit cases are considered, namely, that of light fermions with mL 1, and that of heavy fermions for which mL 1. It is found that both positive and negative energies are obtained for different sets of values of the boundary parameters. As a consequence of our calculation we demonstrate that the sign of the quantum vacuum energy is not
fixed for exchange-symmetric plates (parity-invariant configurations), unlike for electromagnetic and
scalar fields.
