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We calculate the one-loop thermal self-energy of a neutrino in a constant and homogeneous magnetic field to all orders in the magnetic field strength using Schwinger's proper time method. We obtain the dispersion relation under various conditions. ͓S0556-2821͑98͒08618-4͔PACS number͑s͒: 14.60.Pq, 95.30.Cq

We calculate the conversion rate of high-energy neutrinos propagating in constant magnetic field into an electron-W pair (ν → W + e) from the imaginary part of the neutrino self-energy. Using the exact propagators in constant magnetic field, the neutrino self-energy has been calculated to all order in the field within the Weinberg-Salam model. We obtain a compact formula in the limit of B B cr ≡ m 2 /e. We find that above the process threshold E (th) ≈ 2.2·10 16 eV ×(B cr /B) this contribution to the absorption of neutrinos yields an asymptotic absorption length ≈ 1.1 m ×(B cr /B) 2 × (10 16 eV/E).

Using the exact propagators in a constant magnetic field, the neutrino self-energy has been calculated to all orders in the field strength B within the minimal extension of the WeinbergSalam model with massive Dirac neutrinos. A simple and very accurate formula for the selfenergy is obtained, that is valid for 0 ≤ B ≪ m 2 W /e and for neutrino transverse momentum to the magnetic field p ⊥ ≪ m W . I discuss the implications of this finding to the dispersion of massless neutrinos in vacuum and in a charge-symmetric medium, and to the magnetic field induced resonance transitions of massive neutrinos inside supernovae and magnetars, and calculate the neutrino magnetic moment.