In the last decades, the blossoming of experimental breakthroughs in the domain of electron energy loss spectroscopy (EELS) has triggered a variety of theoretical developments. Those have to deal with completely different situations, from atomically resolved phonon mapping to electron circular dichroism passing by surface plasmon mapping. All of them rely on very different physical approximations and have not yet been reconciled, despite early attempts to do so. As an effort in that direction, we report on the development of a scalar relativistic quantum electrodynamic (QED) approach of the inelastic scattering of fast electrons. This theory can be adapted to describe all modern EELS experiments, and under the relevant approximations, can be reduced to any of the last EELS theories. In that aim, we present in this paper the state of the art and the basics of scalar relativistic QED relevant to the electron inelastic scattering. We then give a clear relation between the two once antagonist descriptions of the EELS, the retarded green Dyadic, usually applied to describe photonic excitations and the quasi-static mixed dynamic form factor (MDFF), more adapted to describe core electronic excitations of material. We then use this theory to establish two important EELS-related equations. The first one relates the spatially resolved EELS to the imaginary part of the photon propagator and the incoming and outgoing electron beam wavefunction, synthesizing the most common theories developed for analyzing spatially resolved EELS experiments. The second one shows that the evolution of the electron beam density matrix is proportional to the mutual coherence tensor, proving that quite universally, the electromagnetic correlations in the target are imprinted in the coherence properties of the probing electron beam.

中文翻译：

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在相对论电子束非弹性散射的统一描述中，桥接纳米光学和凝聚态形式学

在过去的几十年中，电子能量损失谱学（EELS）领域的实验性突破不断涌现，引发了各种理论发展。那些必须处理完全不同的情况，从原子分辨的声子映射到通过表面等离子体激元映射通过的电子圆二色性。它们都依赖于非常不同的物理近似值，并且尽管已经进行了早期尝试，但尚未对帐。为了朝这个方向努力，我们报告了快速电子非弹性散射的标量相对论量子电动力学（QED）方法的发展。该理论可以适用于描述所有现代EELS实验，并且在相关近似下可以简化为任何最新的EELS理论。为此，我们在本文中介绍了与电子非弹性散射有关的标量相对论QED的技术现状和基础。然后，我们在EELS的两个曾经拮抗的描述，通常用于描述光子激发的延迟绿色Dyadic和更适合于描述材料的核心电子激发的准静态混合动态形状因数（MDFF）之间给出清晰的关系。然后，我们使用该理论建立两个重要的EELS相关方程。第一个将空间分辨的EELS与光子传播器的虚部以及入射和射出的电子束波函数相关联，综合了为分析空间分辨的EELS实验而开发的最普遍的理论。