度规-仿射几何中的光传播与强度传输
Light propagation and intensity transport in metric-affine geometry
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中文总结 AI 辅助
该研究以U(1)规范不变性和仿射联络射影不变性为原理，构建两个度规-仿射几何下的电磁模型，推导其几何光学极限，证明耦合可改变光传播特性，为相关现象学研究提供形式基础。
中文摘要 AI 辅助
我们研究度规-仿射几何中的电磁波传播，该几何中可能存在挠率与非度规性，且电磁学与时空的耦合不再唯一。我们不先验地选择特定耦合方案，而是以保持标准U(1)规范不变性和仿射联络的射影不变性为指导对称性原理，构建电磁部分。我们引入两个代表性模型：其一，麦克斯韦项由非黎曼不变量构成的标量前置因子修饰；其二，动能项由作为各向异性介质的四阶本构张量修正。我们推导了它们的几何光学极限，证明其耦合可修改有效光锥、改变场振幅与强度的关系、诱导偏振相关的传播，并产生双折射与模式混合。这些结果为更广泛的现象学研究提供了形式基础，该研究将挠率与非度规性和具体度规-仿射背景中的电磁可观测量（包括黑洞成像、双折射透镜、偏振可观测量及光子数守恒的偏离）关联起来。
英文摘要
We study electromagnetic wave propagation in metric--affine geometries, where torsion and non-metricity may be present and the coupling between electromagnetism and spacetime is no longer unique. Rather than choosing a particular coupling prescription a priori, we construct electromagnetic sectors that preserve standard $U(1)$ gauge invariance and projective invariance of the affine connection as guiding symmetry principles. We introduce two representative models, one in which the Maxwell term is dressed by a scalar prefactor built from non-Riemannian invariants, and another in which the kinetic term is modified by a rank--four constitutive tensor acting as an anisotropic medium. We derive their geometric--optics limits and show that their couplings can modify the effective light cone, change the relation between field amplitude and intensity, induce polarization-dependent propagation, and generate birefringence and mode mixing. These results thus provide the formal basis for a broader phenomenological study connecting torsion and non-metricity with electromagnetic observables in concrete metric--affine backgrounds, including black-hole imaging, birefringent lensing, polarization observables, and departures from photon-number conservation.
