标题： 极化辐射传输的重新表述用于天体物理应用（一）。 一种允许非局部 Magnus 解决方案的形式化 显示英文标题

标题： Reformulating polarized radiative transfer for astrophysical applications (I). A formalism allowing non-local Magnus solutions

摘要： 太阳大气通过求解非局部热力学平衡（NLTE）等离子体的偏振辐射转移问题来诊断。 多维NLTE诊断中的一个关键挑战是高效地积分辐射转移方程（RTE），但目前的方法是局部的，即仅限于常数传播矩阵。 本文引入了一种使用Magnus展开进行非局部积分RTE的形式化方法。 我们首先从Lorentz/Poincare群中的旋转（Stokes形式）来表述这个问题，从而说明使用Magnus展开的动机。 通过将后者与传播矩阵的高度详细代数特征相结合，我们推导出一个紧凑的解析演化算子，该算子支持传播矩阵的任意变化，并允许越来越多地考虑Magnus展开的任意阶次。 此外，我们还再次利用Magnus展开重新表述RTE的非齐次部分，并引入了非齐次演化算子的新概念。 这提供了第一个一致、通用且非局部的RTE解析解，而且效率高，并将积分与代数形式解分离。 我们的框架在分析和计算上都得到了验证，导致了一类新的数值辐射转移方法以及加速NLTE计算等潜在应用。 经过少量调整，我们的结果适用于其他在狭义相对论和电磁学中共享Lorentz/Poincare代数的普遍物理问题。 显示英文摘要

摘要： The solar atmosphere is diagnosed by solving the polarized radiative transfer problem for plasmas in Non-Local Thermodynamic Equilibrium (NLTE). A key challenge in multidimensional NLTE diagnosis is to integrate efficiently the radiative transfer equation (RTE), but current methods are local, i.e. limited to constant propagation matrices. This paper introduces a formalism for non-local integration of the RTE using the Magnus expansion. We begin by framing the problem in terms of rotations within the Lorentz / Poincare group (Stokes formalism), motivating the use of the Magnus expansion. By combining the latter with a highly detailed algebraic characterization of the propagation matrix, we derive a compact analytical evolution operator that supports arbitrary variations of the propagation matrix and allows to increasingly consider any order in the Magnus expansion. Additionally, we also reformulate the inhomogeneous part of the RTE, again using the Magnus expansion, and introducing the new concept of inhomogeneous evolution operator. This provides the first consistent, general, and non-local formal solution to the RTE that is furthermore efficient and separates integration from the algebraic formal solution. Our framework is verified analytically and computationally, leading to a new family of numerical radiative transfer methods and potential applications such as accelerating NLTE calculations. With minor adjustments, our results apply to other universal physical problems sharing the Lorentz / Poincare algebra in special relativity and electromagnetism.