Towards a quantum theory of the chiral magnetic effect

We discuss three possible ways of addressing quantum physics behind chiral magnetic effect and electric charge fluctuation patterns in heavy-ion collisions. The first one makes use of P-parity violation probed by local order parameters, the second considers the chiral magnetic effect in the quantum measurement theory framework, and the third way is to study a product of two P-odd contributions. In the latter approach, the relevant form factor is constructed and computed for a weak magnetic field in the confinement region and for free quarks in a strong field. It is shown that the effect is negligible in the former case. We also discuss the saturation effect---the charge fluctuation asymmetry for free fermions reaches a constant value at asymptotically large fields.