Finsler type modification of the Coulomb law

Finsler geometry is a natural generalization of pseudo Riemannian geometry It can be motivated e g by some scenarios of quantum gravity that suggest a modified dispersion relation which could be phrased in terms of Finsler geometry On a Finslerian spacetime the Universality of Free Fall is still satisfied but Local Lorentz Invariance is violated in a way not covered by standard Lorentz Invariance Violation schemes In this talk we describe a Finslerian modification of Maxwell s equations The corrections to the Coulomb potential and to the hydrogen energy levels are computed We find that the Finsler metric corrections yield a splitting of the energy levels Experimental data provide bounds for the Finsler parameters Based on: Itin Yakov Claus L mmerzahl and Volker Perlick Finsler type modification of the Coulomb law Physical Review D 90 12 2014 : 124057