Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2010-07-07
Phys.Rev.D82:105026,2010
Physics
High Energy Physics
High Energy Physics - Phenomenology
17 pages, 5 figures. Typos corrected and references added, PRD Version
Scientific paper
10.1103/PhysRevD.82.105026
The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\vec{E}(\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial differential equations of infinite order for the sixteen irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory (QKT) is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field $E(t)=E_0$ and the Sauter-type electric field $E(t)=E_0\operatorname{sech}^2(t/\tau)$. These analytic solutions translate into corresponding expressions within the DHW formalism and allow to discuss the effect of higher derivatives. We observe that spatial field variations typically exert a strong influence on the components of the Wigner function for large momenta or for late times.
Alkofer Reinhard
Gies Holger
Hebenstreit Florian
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