Chiral effects in gauge theories and the chiral chemical potential

Abstract

The chiral balance is broken as a result of an anomaly relation for the axial current in a strongly magnetized electron–positron gas in QED. The pair creation process, due to the decay of longitudinal axial photons (out of light cone), induces an imbalanced chirality and contributes to a chiral current along the external magnetic field B. In our case, a pseudo‐vector longitudinal mode generates the chiral charge density. A chiral chemical potential is not necessary. Only an electromagnetic chemical potential is introduced, but the chiral effect is valid even when it vanishes. A nonzero fermion mass is assumed, which is usually considered vanishing. The introduction of a chiral chemical potential in the frame of electroweak theory at finite temperature and density is discussed. It is not compatible with the Standard Model, since the spontaneous symmetry breaking prevents the conservation of the weak neutral charge.