Casimir energy of Dirac field in external magnetic field by the method of generalized zeta function M. V. Cougo-Pinto, C. Farina, A. C. Tort Instituto de F´ ısica da UFRJ, CP 68528, Rio de Janeiro, RJ 21945-970 F. A. Farias, M. S. Ribeiro Departamento de F´ ısica da UEFS, Feira de Santana, BA 44031-460 20 de outubro de 2001 Abstract We compute the Casimir energy of a fermionic field under the influence of a uniform magnetic field. We use the generalized zeta function method to calculate the relevant fermionic determinant and show that the Casimir effect can be enhanced by the external magnetic field. The influence of an external magnetic field on the Casimir energy of the Dirac field is here revisited. This influence was firstly studied for an antiperiodic boundary condition by Cougo-Pinto et al. [1]. These authors used Schwinger’s proper-time representation for the effective action and showed that the Casimir effect can be enhanced by a magnetic field. The results for a Dirichlet boundary condition as well as for a periodic boundary condition are given in ref. [2] and for a general condition interpolating periodic and antiperiodic conditions can be found in ref. [3]. Here, we reconsider the boundary conditions assumed in [3], but instead of computing the Casimir energy for the Dirac field as the energy of the Dirac sea, we shall compute the corresponding fermionic determinant through the generalized zeta function method (for a review of this method see ref. [4] and references therein). The generalized boundary condition to be considered here is such that the Dirac field suffers a phase shift, which we call α, each time the variable z is changed by an amount a: ψ (r, θ, z + a) = e iα ψ (r, θ, z) (1) ¯ ψ (r, θ, z + a) = e -iα ¯ ψ (r, θ, z) . (2) For α = π we recover the original antiperiodic boundary condition and with α = 0 we have a periodic boundary condition. For other values of α between 0 and π we have interpolations from the usual periodic to antiperiodic boundary conditions. Methods based on analytical extension, like the generalized zeta function method, usually provide the final answer with a minimum of spurious terms and as such, it is convenient to use it to check results obtained by others methods. In this sense, the purpose of this work is to reobtain the results quoted in ref(s) [1, 2, 3] in the context of the zeta function method. Our starting point is the 1