Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2008-07-07
Phys.Rev.D78:036008,2008
Physics
High Energy Physics
High Energy Physics - Phenomenology
6 pages, 1 figure; References added, minor typos fixed
Scientific paper
10.1103/PhysRevD.78.036008
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, $\Gamma$, and show that they differ. While $w$ is given by the standard Schwinger mechanism result $w$, an infinite series, the pair production rate, $\Gamma$, 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 $\Gamma$ differ.
Cohen Thomas D. .
McGady David A.
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