Extra Dimensions Corrections for Fermionic Casimir Effect in Three Dimensional Box

Abstract

We want to show extra-dimensions corrections for Fermionic Casimir Effect. Firstly, we determined quantization fermion field in Three dimensional Box. Then we calculated the Casimir energy for massless fermionic field confined inside a three-dimensional rectangular box with one compact extra - dimension. We use the MIT bag model boundary condition for the confinement and M 4 × S 1 as the background spacetime. We use the direct mode summation method along with the Abel-Plana formula to compute the Casimir energy. We show analytically the extra-dimension cor rections to the Fermionic Casimir effect to forward a new method of exploring the existence of the extra dimensions of the universe.