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arXiv · 0807.1117

The Schwinger mechanism revisited

Thomas D. Cohen·David A. McGady
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Abstract

The vacuum persistence probability, $P_{vac}(t)$, for a system of charged fermions in a fixed, external, and spatially homogeneous electric field, was derived long ago by Schwinger; $w = -log[P_{vac}(t)]/ (V t)$ has often been identified as the rate at which fermion-antifermion pairs are produced per unit volume due to the electric field. In this paper, we separately compute exact expressions for both $w$ and for the rate of fermion-antifermion pair production per unit volume, $Γ$, and show that they differ. While $w$ is given by the standard Schwinger mechanism result $w$, an infinite series, the pair production rate, $Γ$, is just the first term of that series. Our calculation is done for a system with periodic boundary conditions in the $A_0=0$ gauge but the result should hold for any consistent set of boundary conditions. We discuss, the physical reason why the rates $w$ and $Γ$ differ.

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Thomas D. Cohen, David A. McGady. 2008-08-30. The Schwinger mechanism revisited. https://doi.org/10.1103/physrevd.78.036008

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