高能极限下的非线性三叉戟：非定域性、库仑场和近似
Nonlinear trident in the high-energy limit: Nonlocality, Coulomb field and resummations
摘要：
本文研究了高能极限下激光脉冲中的非线性三叉戟效应，即初始电子在其静止坐标系中所经历的电磁场强度高于Schwinger临界场。在较低能量下，主要贡献来自“两步”部分，但在高能量极限下，主要贡献来自一步项。我们得到新的近似，解释三叉戟的高能量极限和库仑场对生产之间的关系，以及Weizsäcker-Williams近似的作用，为什么它不同意的局部恒定场近似的高$χ$限制。我们还表明，下一个领导秩序的大$a_0$扩展，在高能量极限，非本地的，是非常重要的，即使是相当大的$a_0$的数字。我们表明，小- $a_0$扰动系列具有有限的收敛半径，但使用Padé-共形方法，我们得到的mammations，超出了收敛半径，并有一个大的数值重叠与大- $a_0$近似。我们使用Borel-Padé-保角方法对小- $χ$展开式进行求和，得到了直到非常大的$χ$的高精度.我们还使用更新的remation方法的基础上超几何/Meijer-G和合流超几何函数。
英文摘要：
We study nonlinear trident in laser pulses in the high-energy limit, where the initial electron experiences, in its rest frame, an electromagnetic field strength above Schwinger's critical field. At lower energies the dominant contribution comes from the "two-step" part, but in the high-energy limit the dominant contribution comes instead from the one-step term. We obtain new approximations that explain the relation between the high-energy limit of trident and pair production by a Coulomb field, as well as the role of the Weizsäcker-Williams approximation and why it does not agree with the high-$χ$ limit of the locally-constant-field approximation. We also show that the next-to-leading order in the large-$a_0$ expansion is, in the high-energy limit, nonlocal and is numerically very important even for quite large $a_0$. We show that the small-$a_0$ perturbation series has a finite radius of convergence, but using Padé-conformal methods we obtain resummations that go beyond the radius of convergence and have a large numerical overlap with the large-$a_0$ approximation. We use Borel-Padé-conformal methods to resum the small-$χ$ expansion and obtain a high precision up to very large $χ$. We also use newer resummation methods based on hypergeometric/Meijer-G and confluent hypergeometric functions.
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