Fermionic vacuum energy from a Nielsen-Olesen vortex

We calculate the vacuum energy of a spinor field in the background of a Nielsen-Olesen vortex. We use the method of representing the vacuum energy in terms of the Jost function on the imaginary momentum axis. We use zeta-functional regularization. Renormalization is then carried out with the help of the heat kernel expansion. This method gives rise to well convergent sums and integrals which allow for an efficient numerical calculation of the vacuum energy even in the case when the background is not known analytically but only numerically. The vacuum energy is calculated for several choices of the parameters and, as it turns out, is small compared to the classical energy.