Abstract
We study the time evolution of the chirality imbalance $n_5$ and the chiral magnetic effect (CME) under the external parallel electromagnetic fields without assuming the artificial chiral asymmetric source. We adopt the time-dependent Sauter-type electric and constant magnetic field, and obtain analytical solutions of the Dirac equation for a massive fermion. We use the point-split regularization to calculate the vacuum contribution in the gauge invariant way. As a result, we find that $n_5$ and CME current increase substantially as the electric field increases, and stay finite after the electric field is switched off. The chirality imbalance and CME current are shown to consist of a dominant contribution, which is essentially proportional to relativistic velocity, and a small oscillating part. We find a simple analytical relation between $n_5$ and the fermion pair-production rate from the vacuum. We also discuss dynamical origin of the chirality imbalance in detail.
Highlights
Roles of the chiral anomaly have attracted considerable theoretical and experimental interest in various subjects of physics
We present our numerical results for the time evolution of the vacuum expectation values of the chirality imbalance and chiral magnetic effect (CME) in Sec
We have studied the chirality imbalance of the vacuum under the time-independent magnetic field and the Sautertype pulsed electric field
Summary
Roles of the chiral anomaly have attracted considerable theoretical and experimental interest in various subjects of physics. [19], the CME current is suppressed in the insulator phase, which may correspond to the chiral symmetry breaking phase For these purposes, we study time evolution of the chirality imbalance n5 and the chiral magnetic effect in the vacuum under the electromagnetic field solving the Dirac equation analytically without initial chiral chemical potential [20]. We consider the vacuum state (zero temperature and zero fermion chemical potential) with external parallel electromagnetic fields, which provide the chirality imbalance of the fermion number density due to the chiral anomaly.
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