Abstract
The chiral magnetic effect is concisely derived by employing the Wigner function approach in the chiral fermion system. Subsequently, the chiral magnetic effect is derived by solving the Landau levels of chiral fermions in detail. The second quantization and ensemble average leads to the equation of the chiral magnetic effect for righthand and lefthand fermion systems. The chiral magnetic effect arises uniquely from the contribution of the lowest Landau level. We carefully analyze the lowest Landau level and find that all righthand (chirality is +1) fermions move along the direction of the magnetic field, whereas all lefthand (chirality is −1) fermions move in the opposite direction of the magnetic field. Hence, the chiral magnetic effect can be explained clearly using a microscopic approach.
Highlights
Quark gluon plasma (QGP) can be created in high energy heavy ion collisions, which is a extremely hot and dense matter
Very huge magnetic field can be produced for high energy peripheral collisions [1,2,3]
One of the predictions in QGP is that positively charged particles and negatively charged particles will seperate along the direction of magnetic field, which is related to chiral magnetic effect (CME) [4,5,6]
Summary
Quark gluon plasma (QGP) can be created in high energy heavy ion collisions, which is a extremely hot and dense matter. Due to the mass m of Dirac fermion, the physical picture of CME for massive Dirac fermion system is not as clear as massless fermion case, because the physical meaning of chiral chemical potential μ5 for massive fermion case is not very clear To see this issue clearly, we list the lowest Landau level as follows (We set the homogeneous magnetic background B = Bez along z-axis and assume eB > 0, which is appropriate for following sections), φ0. It is very difficult to obtain a net electric current along the magnetic field direction from the picture of the lowest Landau level for massive fermion case.
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