We discuss spontaneous symmetry breaking in the presence of a new type of symmetric potential based on Fresnel integrals which give an infinite number of minima. Several interesting points were raised, in particular the emergence of massive Goldstone boson and an enhancement of the photon mass. The new theory depends on discrete numbers n, N ∈ Z and hence a large family of massive particles may be obtained filling the gap between the electroweak scale and the Planck scale in the standard model.