Test of CPT and Lorentz invariance from muonium spectroscopy.

Following a suggestion from Kostelecký et al., we evaluated a test of CPT and Lorentz invariance from the microwave spectroscopy of muonium. Hamiltonian terms beyond the standard model violating CPT and Lorentz invariance would contribute frequency shifts deltanu(12) and deltanu(34) to nu(12) and nu(34), the two transitions involving muon spin flip, which were precisely measured in ground state muonium in a strong magnetic field of 1.7 T. The shifts would be indicated by anticorrelated oscillations in nu(12) and nu(34) at the Earth's sidereal frequency. No time dependence was found in nu(12) or nu(34) at the level of 20 Hz, limiting the size of some CPT and Lorentz-violating parameters at the level of 2x10(-23) GeV.