  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 e B <<
m_\ell^2, where m_\ell is the charged-lepton mass corresponding to the neutrino
flavor \nu_\ell, and we consider a "moderate field" m_\ell^2 << e B << m_W^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 (e B)^2 and thus comparable to the
contribution of the magnetized plasma.
