Generation of cosmic magnetic fields in electroweak plasma
  We study the generation of strong magnetic fields in magnetars and in the
early universe. For this purpose we calculate the antisymmetric contribution to
the photon polarization tensor in a medium consisting of an electron-positron
plasma and a gas of neutrinos and antineutrinos, interacting within the
Standard Model. Such a contribution exactly takes into account the temperature
and the chemical potential of plasma as well as the photon dispersion law in
this background matter. It is shown that a nonvanishing Chern-Simons parameter,
which appears if there is a nonzero asymmetry between neutrinos and
antineutrinos, leads to the instability of a magnetic field resulting to its
growth. We apply our result to the description of the magnetic field
amplification in the first second of a supernova explosion. It is suggested
that this mechanism can explain strong magnetic fields of magnetars. Then we
use our approach to study the cosmological magnetic field evolution. We find a
lower bound on the neutrino asymmetries consistent with the well-known Big Bang
nucleosynthesis bound in a hot universe plasma. Finally we examine the issue of
whether a magnetic field can be amplified in a background matter consisting of
self-interacting electrons and positrons.
