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.
Highlights
Quantum electrodynamics (QED) of strong electromagnetic (EM) fields has been studied for a very long time [1]
We have derived the equation of motion for the equal-time Wigner function, the 16 components of which, the so-called DHW functions, have definite physical meanings
We obtained an analytic solution for the system of partial differential equations (PDEs) for the DHW functions
Summary
Quantum electrodynamics (QED) of strong electromagnetic (EM) fields has been studied for a very long time [1]. The electric field in heavy-ion collisions can reach eE ∼ m2πc3=ħ ≫ eEc at the RHIC [2], which provides realistic conditions to study pair production. Analytical calculations show that a magnetic field which is parallel to the electric field can increase the pair-production rate [16,37,38,39,40]. The enhancement of the pair-production rate due to parallel magnetic fields has been studied in string theory [41,42,43].
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