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We study the Schwinger effect, in which the external field having a spatiotemporal profile creates electron-positron pairs via multidimensional quantum tunneling.
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C. K. Dumlu and G. V. Dunne, “The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses,” Phys. Rev. Lett. 104
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Cited in the paper.
The leading order approximation for the current, ∂ ν F 1 ν ( ν = 0 , 3 ) \partial_{\nu}F_{1\nu}(\nu=0,3) can be given by using the classical trajectories. For the closed tunneling orbits, where σ ≫ m − 1 \sigma\gg m^{-1} , we have | ∂ ν F 1 ν | ≪ | F 1 ν x ˙ ν | |\partial_{\nu}F_{1\nu}|\ll|F_{1\nu}\dot{x}_{\nu}| . But if the external field gets localized down to the scale of vacuum fluctuations, magnitude of the current becomes at the order of field strength, and significantly contributes to the commutator, [ d x ^ 1 / d u , D ^ 2 ] [d\,\hat{x}_{1}/du,\,\not{\hskip-2.84544pt\hat{D}^{2}}]
Cited in the paper.
C. K. Dumlu and G. V. Dunne, “Complex Worldline Instantons and Quantum Interference in Vacuum Pair Production ,” Phys. Rev. D 84
2011
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A. Ilderton “Localisation in worldline pair production and lightfront zero-modes ,” JHEP 1409
2015
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