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This talk discusses theoretical aspects of tests of CPT and Lorentz Symmetry that will in principle be possible with trapped antihydrogen. The framework is the standard-model extension, which admits minuscule violations of CPT and Lorentz symmetry in a general manner without giving up other features of the standard model of particle physics. Spectroscopic transitions in hydrogen and antihydrogen that exhibit leading-order effects are identified. Such comparisons of spectral frequencies in antimatter with the corresponding frequencies in regular matter will bound parameter combinations that are not accessible with regular-matter atoms alone.

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