Lorentz-violating spinor electrodynamics and Penning traps

The prospects are explored for testing Lorentz- and $CPT$-violating quantum electrodynamics in experiments with Penning traps. We present the Lagrange density of Lorentz-violating spinor electrodynamics with operators of mass dimensions up to 6, and we discuss some of its properties. The theory is used to derive Lorentz- and $CPT$-violating perturbative shifts of the energy levels of a particle confined to a Penning trap. Observable signals are discussed for trapped electrons, positrons, protons, and antiprotons. Existing experimental measurements on anomaly frequencies are used to extract new or improved bounds on numerous coefficients for Lorentz and $CPT$ violation, using sidereal variations of observables and comparisons between particles and antiparticles.