Test for the $CPT$ invariance of bound states in QED and production of muonium or antimuonium in electron or positron scattering by nuclei

The possibility of testing the QED $CPT$ invariance of bound states is analyzed for muonium or antimuonium produced in electron or positron scattering by nuclei. The number of muonium production events is estimated for modern accelerators. The method of muonium detection by measuring oscillations appearing in the decay curve owing to the interference of the muonium ground and excited states is discussed.