Laboratory tests of Lorentz and $CPT$ symmetry with muons

The prospects are explored for testing Lorentz and $CPT$ symmetry in the muon sector via the spectroscopy of muonium and various muonic atoms, and via measurements of the anomalous magnetic moments of the muon and antimuon. The effects of Lorentz-violating operators of both renormalizable and nonrenormalizable dimensions are included. We derive observable signals, extract first constraints from existing data on a variety of coefficients for Lorentz and $CPT$ violation, and estimate sensitivities attainable in forthcoming experiments. The potential of Lorentz violation to resolve the proton radius puzzle and the muon anomaly discrepancy is discussed.