Extra-dimension effects on the fermion-induced quantum energy in the presence of a constant magnetic field

We consider a U(1) gauge field theory with fermion fields (or with scalar fields) that live in a space with {delta} extra compact dimensions, and we compute the fermion-induced quantum energy in the presence of a constant magnetic field, which is directed towards the x{sub 3} axis. Our motivation is to study the effect of extra dimensions on the asymptotic behavior of the quantum energy in the strong field limit (eB>>M{sup 2}), where M=1/R. We see that the weak logarithmic growth of the quantum energy for four dimensions is modified by a rapid power growth in the case of the extra dimensions.