Magnetic field effects on lagrangians and neutrino self-energies in the Salam-Weinberg theory in arbitrary gauges

An analytic expression for the W-field propagator of the Salam-Weinberg theory in a constant magnetic field is obtained. To obtain the result in an arbitrary weak (ξ) gauge, gauge-fixing terms (different from those usually chosen) must be introduced which are manifestly invariant under electromagnetic gauge transformations. This W-propagator is then used to calculate an expression for the neutrino self-energy in a magnetic field. The result implies an effective neutrino “mass” analogous to that found in the MSW effect. Such a “mass” may be observable in collapsing supernovae. The effective electromagnetic lagrangian is found in an arbitrary (ξ) gauge and shown to be gauge invariant.