Neutrino dispersion in external magnetic fields

We calculate the neutrino self-energy operator {sigma}(p) in the presence of a magnetic field B. In particular, we consider the weak-field limit eB<<m{sub l}{sup 2}, where m{sub l} is the charged-lepton mass corresponding to the neutrino flavor {nu}{sub l}, and we consider a 'moderate field' m{sub l}{sup 2}<<eB<<m{sub W}{sup 2}. Our results differ substantially from the previous literature. For a moderate field, we show that it is crucial to include the contributions from all Landau levels of the intermediate charged lepton, not just the ground state. For the conditions of the early universe where the background medium consists of a charge-symmetric plasma, the pure B-field contribution to the neutrino dispersion relation is proportional to (eB){sup 2} and thus comparable to the contribution of the magnetized plasma.