$CPT$ and Lorentz Tests in Hydrogen and Antihydrogen

Signals for CPT and Lorentz violation at the Planck scale may arise in hydrogen and antihydrogen spectroscopy. We show that certain 1S-2S and hyperfine transitions can exhibit theoretically detectable effects unsuppressed by any power of the fine-structure constant. {copyright} {ital 1999} {ital The American Physical Society}