  This dissertation studies the quantum anomalous effects on the description of
high energy electrodynamics. We argue that on the temperatures comparable to
the electroweak scale, characteristic for the early Universe and objects like
neutron stars, the description of electromagnetic fields in conductive plasmas
needs to be extended to include the effects of chiral anomaly. It is
demonstrated that chiral effects can have a significant influence on the
evolution of magnetic fields, tending to produce exponential amplification,
creation of magnetic helicity from initially non-helical fields, and can lead
to an inverse energy transfer. We further discuss the modified
magnetohydrodynamic equations around the electroweak transition. The obtained
solutions demonstrate that the asymmetry between right-handed and left-handed
charged fermions of negligible mass typically grows with time when approaching
the electroweak crossover from higher temperatures, until it undergoes a fast
decrease at the transition, and then eventually gets damped at lower
temperatures in the broken phase. At the same time, the dissipation of magnetic
fields gets slower due to the chiral effects. We furthermore report some first
analytical attempts in the study of chiral magnetohydrodynamic turbulence.
Using the analysis of simplified regimes and qualitative arguments, it is shown
that anomalous effects can strongly support turbulent inverse cascade and lead
to a faster growth of the correlation length, when compared to the evolution
predicted by the non-chiral magnetohydrodynamics. Finally, the discussion of
relaxation towards minimal energy states in the chiral magnetohydrodynamic
turbulence is also presented.
