Abstract
The semiclassical approximation of the worldline path integral is a powerful tool to study nonperturbative electron-positron pair creation in spacetime-dependent background fields. Finding solutions of the classical equations of motion, i.e., worldline instantons, is possible analytically only in special cases, and a numerical treatment is nontrivial as well. We introduce a completely general numerical approach based on an approximate evaluation of the discretized path integral that easily and robustly gives the full semiclassical pair production rate in nontrivial multidimensional fields, and apply it to some example cases.
Highlights
We introduce a completely general numerical approach based on an approximate evaluation of the discretized path integral that and robustly gives the full semiclassical pair production rate in nontrivial multidimensional fields, and apply it to some example cases
A currently unconfirmed prediction of quantum electrodynamics is that of nonperturbative electron-positron pair creation in the presence of a strong electric field [1,2,3]
We have introduced a new approach to numerically implement the worldline instanton method for electronpositron pair creation
Summary
A currently unconfirmed prediction of quantum electrodynamics is that of nonperturbative electron-positron pair creation in the presence of a strong electric field [1,2,3]. Our method is based on discretization as well, we use an instanton approach to compute the integrals instead of statistical sampling This instanton approach is a semiclassical approximation based on a saddlepoint approximation of the worldline path integral where m2=ðqEÞ plays the role of the large expansion parameter. Both Feynman and Schwinger mentioned the fourdimensional particle’s equations of motion in the classical limit, but the first explicit mention of an instanton approximation to the (Euclidean) worldline path integral was given by Affleck, Alvarez and Manton [21] They derived the pair production rate for a constant homogeneous background field in a way that is very similar to the method used today.
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