Hypermagnetic Field Effects in the Thermal Bath of Chiral Fermions
  The dispersion relations for leptons in the symmetric phase of the electroweak model in the presence of a constant hypermagnetic field are investigated. The one-loop fermion self-energies are calculated in the lowest Landau level approximation and used to show that the hypermagnetic field forbids the generation of the ''effective mass'' found as a pole of the fermions' propagators at high temperature and zero fields. In the considered approximation leptons behave as massless particles propagating only along the direction of the external field. The reported results can be of interest for the cosmological implications of primordial hypermagnetic fields. 
J. Cannellos, E. J. Ferrer, and V. de la Incera