Momentum correlation in pair production by spacetime dependent fields from scattered wave functions

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1. Verfasser: Torgrimsson, Greger
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Veröffentlicht: 2025
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author Torgrimsson, Greger
author_facet Torgrimsson, Greger
contents We consider Sauter-Schwinger pair production by electric fields that depend on both time and space, $E(t,z)$ and $E(t,x,y)$. For space-independent fields, $E(t)$, momentum conservation, $δ({\bf p}+{\bf p}')$, fixes the positron momentum, ${\bf p}'$, in terms of the electron momentum, ${\bf p}$. For $E(t,z)$, on the other hand, $p_z$ and $p'_z$ are independent. However, previous exact-numerical studies have considered only the probability as a function of a single momentum variable, $P(p_z)$, $P(p'_z)$ or $P(p'_z-p_z)$, but not the correlation $P(p_z,p'_z)$. In this paper, we show how to obtain $P(p_z,p'_z)$ by solving the Dirac equation numerically. To do so, we split the wave function into a background and a scattered wave, $ψ(t,{\bf x})=ψ_{\rm back.}(t,{\bf x})+ψ_{\rm scat.}(t,{\bf x})$, where $ψ_{\rm back.}\propto\exp(\pm ipx+\text{gauge term})$. $ψ_{\rm scat.}$ vanishes outside a past light cone and is obtained by solving $(iγ^μD_μ-m)ψ_{\rm scat.}=-(iγ^μD_μ-m)ψ_{\rm back.}$ backwards in time starting with $ψ_{\rm scat.}(t\to+\infty,{\bf x})=0$.
format Preprint
id arxiv_https___arxiv_org_abs_2509_17770
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Momentum correlation in pair production by spacetime dependent fields from scattered wave functions
Torgrimsson, Greger
High Energy Physics - Phenomenology
High Energy Physics - Theory
We consider Sauter-Schwinger pair production by electric fields that depend on both time and space, $E(t,z)$ and $E(t,x,y)$. For space-independent fields, $E(t)$, momentum conservation, $δ({\bf p}+{\bf p}')$, fixes the positron momentum, ${\bf p}'$, in terms of the electron momentum, ${\bf p}$. For $E(t,z)$, on the other hand, $p_z$ and $p'_z$ are independent. However, previous exact-numerical studies have considered only the probability as a function of a single momentum variable, $P(p_z)$, $P(p'_z)$ or $P(p'_z-p_z)$, but not the correlation $P(p_z,p'_z)$. In this paper, we show how to obtain $P(p_z,p'_z)$ by solving the Dirac equation numerically. To do so, we split the wave function into a background and a scattered wave, $ψ(t,{\bf x})=ψ_{\rm back.}(t,{\bf x})+ψ_{\rm scat.}(t,{\bf x})$, where $ψ_{\rm back.}\propto\exp(\pm ipx+\text{gauge term})$. $ψ_{\rm scat.}$ vanishes outside a past light cone and is obtained by solving $(iγ^μD_μ-m)ψ_{\rm scat.}=-(iγ^μD_μ-m)ψ_{\rm back.}$ backwards in time starting with $ψ_{\rm scat.}(t\to+\infty,{\bf x})=0$.
title Momentum correlation in pair production by spacetime dependent fields from scattered wave functions
topic High Energy Physics - Phenomenology
High Energy Physics - Theory
url https://arxiv.org/abs/2509.17770