Overview of the standard model extension: Implications and phenomenology of Lorentz violation

The Standard Model Extension (SME) provides the most general observer-independent field theoretical framework for investigations of Lorentz -violation. The SME lagrangian by definition, contains all Lorentz-violating interaction terms that can be written as observer scalars and that involve particle fields in the Standard Model and gravitational fields in a generalized theory of gravity. This includes all possible terms that could arise from a process of spontaneous Lorentz violation in the context of a more fundamental theory, as well as terms that explicitly break Lorentz symmetry. An overview of the SME is presented, including its motivations and construction. Some of the theoretical issues arising in the case of spontaneous Lorentz violation are discussed, including the question of what happens to the Nambu-Goldstone modes when Lorentz symmetry is spontaneously violated and whether a Higgs mechanism can occur. A minimal version of the SME in flat Minkowski spacetime that maintains gauge invariance and power-counting renormalizability is used to search for leading-order signals of Lorentz violation. Recent Lorentz tests in QED systems are examined, including experiments with photons, particle and atomic experiments, proposed experiments in space, and experiments with a spin-polarized torsion pendulum.