Abstract
The prospects of tests of CPT symmetry using precision spectroscopy of antihydrogen are discussed with special emphasis on the ground-state hyperfine structure, a measurement of which is the aim of the ASACUSA collaboration at the AD/ELENA facility of CERN. Ongoing parallel experiments using hyperfine spectroscopy of hydrogen and deuterium aiming at studying Lorentz invariance by determining coefficients of the Standard Model Extension framework are described.
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