四维德西特时空中Bopp-Podolsky电动力学的推迟格林函数
Retarded Green Function For Bopp--Podolsky Electrodynamics in Four-Dimensional De Sitter Spacetime
AI总结：
该研究在四维德西特时空中分析经典Bopp-Podolsky电动力学，推导其横向推迟格林函数，揭示麦克斯韦与质量矢量sector的奇异性抵消机制，得到规范不变场强核等结果，还验证了库仑发散抵消等性质。
摘要：
我们研究四维德西特时空中的经典Bopp-Podolsky（BP）电动力学，重点关注其横向推迟格林函数和规范不变的电磁响应。由于德西特时空是最大对称的，其矢量格林函数可在有限的不变双张量基中进行协变展开，标量系数仅取决于不变间隔。对于守恒源，四阶场算子可分解为麦克斯韦算子和质量矢量算子，从而将BP推迟核表示为两者横向格林函数的差值。利用不变双张量分解，我们将传播子方程简化为超几何主方程，并确定其解的分布结构。麦克斯韦 sector 和质量矢量 sector 共有的主导短程奇异性相互抵消，仅留下对数主奇异性和软化的矢量势波前。经过一次旋度运算后，规范不变的场强核包含零锥δ分布和规则类时尾。光滑的麦克斯韦主尾被旋度运算湮灭，因此内部电磁尾完全由质量 sector 产生。我们还推导了精确的视界正则静态势，证明了库仑发散的抵消，恢复了平直空间BP势，并构建了广义高斯定律。在全局德西特时空中，空间截面的紧致性要求总电荷为零；我们采用具有光滑因子化初值的对跖电荷构型来实现这一约束。本分析为经典分析，未假设量子Lee-Wick轮廓或偏好的德西特真空。
英文摘要：
We study classical Bopp--Podolsky (BP) electrodynamics on four-dimensional de Sitter spacetime, focusing on its transverse retarded Green function and gauge-invariant electromagnetic response. Because de Sitter spacetime is maximally symmetric, its vector Green functions admit a covariant expansion in a finite basis of invariant bitensors, with scalar coefficients depending only on the invariant separation. For conserved sources, the fourth-order field operator factorizes into Maxwell and massive-vector operators, yielding the BP retarded kernel as the difference of their transverse Green functions. Using the invariant bitensor decomposition, we reduce the propagator equations to a hypergeometric master equation and determine the distributional structure of its solution. The common leading short-distance singularity of the Maxwell and massive-vector sectors cancels, leaving a logarithmic master singularity and a softened vector-potential wavefront. After one curl, the gauge-invariant field-strength kernel contains a null-cone delta distribution and a regular timelike tail. The smooth Maxwell master tail is annihilated by the curl, so the interior electromagnetic tail is generated entirely by the massive sector. We also derive an exact horizon-regular static potential, demonstrate the cancellation of the Coulomb divergence, recover the flat-space BP potential, and formulate the generalized Gauss law. On global de Sitter spacetime, the compactness of the spatial sections requires the total charge to vanish; we implement this constraint using an antipodal charge configuration with smooth factorized initial data. The analysis is classical and does not assume a quantum Lee--Wick contour or a preferred de Sitter vacuum.
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