Untangling Coefficients for Lorentz Violation

Abstract

bμ, cμv, ... for each particle species. These may be thought of as vectors and tensors that are nonzero even in a vacuum. An experiment that is, in some sense, aligned with one of these may give different results from an experiment that is not aligned, and therefore the existence of these vectors and tensors violates Lorentz symmetry. We focus in this work on the cμv tensor for electrons, which perturbs the electron’s energy-momentum dispersion relation away from its conventional expression. The perturbed dispersion relation implies, in turn, that an electron’s kinetic energy will depend on its direction of travel and speed; for example, in a suitable limit, the kinetic energy of a free electron with velocity is given by , where c represents the matrix of cjk. This orientation dependence constitutes a violation of Lorentz symmetry. Detailed formulas for these perturbations are cumbersome and beyond the scope of this paper, but may be found in the literature (Colladay & Kostelecky, 2001). Some experimental signals involve only a single SME coefficient; however, most involve linear combinations of multiple coefficients. When there are enough linearly independent combinations of coefficients that have been bounded, we may extract bounds on the individual coefficients that appear. In this work, we derive a method for extracting such bounds and apply it to the cμv coefficients that are associated with electrons.