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arXiv · 1812.01146

Wigner function and pair production in parallel electric and magnetic fields

Xin-li Sheng·Ren-hong Fang·Qun Wang·Dirk H. Rischke
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Abstract

We derive analytical formulas for the equal-time Wigner function in an electromagnetic field of arbitrary strength. While the magnetic field is assumed to be constant, the electric field is assumed to be space-independent and oriented parallel to the magnetic field. The Wigner function is first decomposed in terms of the so-called Dirac-Heisenberg-Wigner (DHW) functions and then the transverse-momentum dependence is separated using a new set of basis functions which depend on the quantum number $n$ of the Landau levels. Equations for the coefficients are derived and then solved for the case of a constant electric field. The pair-production rate for each Landau level is calculated. In the case of finite temperature and chemical potential, the pair-production rate is suppressed by Pauli's exclusion principle.

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Xin-li Sheng, Ren-hong Fang, Qun Wang, Dirk H. Rischke. 2018-12-04. Wigner function and pair production in parallel electric and magnetic fields. https://doi.org/10.1103/physrevd.99.056004

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