从共形变换得到的飞行焦点中的散射与耗尽
Scattering and depletion in a flying focus from conformal transformations
AI总结：
通过共形变换将平面波转化为飞行焦点场，揭示了在该场中无质量波方程的解为Volkov解的共形变换，从而能直接计算完全耗尽飞行焦点光束的光子发射振幅，为强场QED计算引入聚焦效应提供了新方法。
摘要：
我们证明飞行焦点场可通过平面波的复共形变换获得，且在所得到的场中无质量波方程的解相应地为Volkov解的共形变换。这导致结果为：在完全耗尽的飞行焦点光束中，光子发射振幅可通过相应平面波振幅对某些动量变量取简单高斯平均直接计算。实际上，这为在强场QED计算中引入聚焦效应提供了'免费'的方法。这些结果扩展到包含仅部分耗尽的散射振幅，并在反自对偶极限下讨论了一些初步结果。
英文摘要：
We show that flying focus fields can be obtained from complex conformal transformation of plane waves, and that solutions of the massless wave equation in the so-obtained fields are, correspondingly, conformal transformations of the Volkov solutions. This leads to the result that photon emission amplitudes in a totally depleting flying focus beam may be computed directly from the corresponding plane wave amplitudes by taking a simple Gaussian average over certain momentum variables. In effect, this gives a way of introducing focussing effects into strong-field QED calculations `for free'. The extension of these results to scattering amplitudes including only partial depletion is discussed and some first results presented in the anti-self-dual limit.
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