光子相对论性动理学理论的几何表述
Geometric formulation for the relativistic kinetic theory of photons
AI总结：
本研究为光子相对论性动理学理论构建几何基础，通过类Hodge对偶方法为退化诱导度规的光锥丛构造体元，建立完全协变的光子Boltzmann方程，实现物理分布的一致定义并得到与有质量粒子形式一致的流体力学量。
AI中文摘要：
我们为光子动理学理论提供了几何基础。尽管光锥丛$\Gamma_0^+$上的诱导度规$\hat h$是退化的，会导致相应体元消失，但我们仍可采用类似Hodge对偶（霍奇对偶）的方法，为光锥丛构造体元$\eta_{\Gamma_0^+}$。基于该几何结构$(\Gamma^+_0,\eta_{\Gamma_0^+},\hat h)$，我们建立了光子的完全协变Boltzmann方程（玻尔兹曼方程）。更重要的是，体元与诱导度规以非平凡方式关联，使得物理分布能够被一致定义。由此得到了相应的流体力学量及其散度，其形式与有质量粒子情形下的形式相同。
英文摘要：
We provide a geometric foundation for the kinetic theory of photons. Although the induced metric $\hat h$ on the light cone bundle $Γ_0^+$ is degenerate, which causes the corresponding volume element to vanish, we can still use a method similar to the Hodge dual to construct a volume element $η_{Γ_0^+}$ for the light cone bundle. Based on this geometric structure $(Γ^+_0,η_{Γ_0^+},\hat h)$, we establish the fully covariant Boltzmann equation for photons. More importantly, the volume element and the induced metric are linked in a nontrivial way, which allows the physical distributions to be defined consistently. This yields the corresponding hydrodynamic quantities and their divergences, which take the same form as in the case of massive particles.
