Low-energy effects in brane worlds: Liennard–Wiechert potentials and Hydrogen Lamb shift

Testing extra dimensions at low-energies may lead to interesting effects. In this work a test point charge is taken to move uniformly in the 3D subspace of a (3 + n)-brane embedded in a (3 + n + 1)-space with n compact and one warped infinite spatial extra dimensions. We found that the electromagnetic potentials of the point charge match standard Liennard–Wiechert’s at large distances but differ from them close to it. These are finite at the position of the charge and produce finite self-energies. We also studied a localized Hydrogen atom and take the deviation from the standard Coulomb potential as a perturbation. This produces a Lamb shift that is compared with known experimental data to set bounds for the parameter of the model. This work provides details and extends results reported in a previous Letter. We are pleased to dedicate this work to Professor Octavio Obregón on occasion of his 60th birthday. H. A. Morales-Técotl is an associate member of the Abdus Salam ICTP, Trieste Italy.