Abstract
A mass-shift of the axion propagating in an external constant homogenious magnetic field is calculated. The contributions via an electron loop and a virtual photon are examined. It is shown that the virtual photon contribution dominates substantially over the electron-loop one. Under the conditions of the early Universe the electron-loop contribution to the massless axion mass-shift is equal to zero while the virtual photon contribution is finite and can be of order of the recent restrictions on the axion mass.
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