Spectroscopy of the hydrogen and anti-hydrogen atoms in external fields

The spectroscopical properties of hydrogen (H) and anti-hydrogen (11) atoms in external electric and magnetic fields are discussed. This problem became important in connection with the recent experimental success in production of H atoms. The main features of these experiments are briefly reviewed. The proposals for the search of the CPT violation via comparison of the H and H spectra are shortly discussed. The spectroscopical differences between H and 11 atoms in external magnetic fields and in parallel magnetic and electric fields are described in detail. It is proven that the positions of the maxima of the frequency distributions for transition probabilities in external electric field for H and H atoms will deviate if the non-resonant corrections to the Lorentz line profile are taken into account.