AI 中文总结
通过几何推导得出平坦空间和全局 AdS 中李纳-维谢尔场，强调对映匹配起源。在平坦空间利用源类时测地线中心坐标求匀速运动电荷场，在 AdS 中从中心静态麦克斯韦解出发重构场，给出 AdS 类似库仑李纳-维谢尔场及相关特性。
AI 中文摘要
我们给出了平坦空间和全局反德西特空间（AdS）中李纳 - 维谢尔场的几何推导，强调了对映匹配的起源。在平坦空间中，通过使用以源类时测地线为中心的坐标来获得匀速运动电荷的场，此时电荷静止且解为普通库仑场。只有在将这个静态解重写为非中心框架后，零无穷远处主导数据的非平凡角依赖性才会出现，从而使对映匹配条件变得透明。我们将相同的构造扩展到全局AdS，其中匀速运动被沿类时测地线的运动所取代。从AdS中心的静态麦克斯韦解出发，我们使用适应测地线的坐标和嵌入空间不变量来重构任意全局坐标下的场。这产生了库仑李纳 - 维谢尔场的封闭形式的AdS类似物，包括规范不变分量$F_{\rho\tau}$。我们表明体场满足精确的对映协变性，并且其零边缘极限再现了在$\mathscr I^+*-$和$\mathscr I^-*+$处库仑数据之间的标准平坦空间对映匹配关系。我们还描述了库仑种子的镜像电荷解释，给出了库仑场、对映匹配以及从AdS到平坦空间极限的统一图景。
英文摘要
We present a geometric derivation of Liénard--Wiechert fields in flat-space and AdS, emphasizing the origin of antipodal matching. In flat-space, the field of a uniformly moving charge is rewritten in coordinates centered on the source timelike geodesic. In this frame the charge is at rest and the solution is Coulombic, so the matching of the leading data at null infinity arises from describing a static field in a non-centered frame. We extend this construction to global AdS, where uniform motion is replaced by motion along a timelike geodesic. Starting from the static Coulomb solution at the center, we reconstruct the field of a freely moving charge in arbitrary global coordinates using embedding-space invariants. The resulting closed-form field obeys exact antipodal covariance in the bulk, and its boundary null-fringe limit reproduces the usual flat-space antipodal matching relation. We also describe an image-charge interpretation: the flat-space Coulomb field is represented after conformal compactification by an image singularity at spatial infinity, while the AdS Coulomb seed may be viewed as a charge together with an opposite image charge in a reflected copy. Together, these perspectives give a unified picture of Coulombic Liénard--Wiechert fields, antipodal matching, and the AdS-to-flat-space limit.
Comments51+7 pages, 5 figures, references added
