The Schwinger mechanism revisited

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; $w=-log[P_{vac}(t)]/(Vt)$ 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.

6 pages, 1 figure; References added, minor typos fixed

References in corpus (6)

• Vacuum instability in external fields
• Schwinger Pair Production in Electric and Magnetic Fields
• Derivative Expansion of the Effective Action for QED in 2+1 and 3+1 dimensions
• Quantum Back Reaction on a Classical Field
• Electron-positron pair creation in a vacuum by an electromagnetic field in 3+1 and lower dimensions
• Flavor Condensate and Vacuum (In-)Stability in QED_(2+1)

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