We review the general construction of distribution functions for gases of fermions and bosons (photons), emphasizing the similarities and differences between both cases. The central object which describes polarization for photons is a tensor-valued distribution function, whereas for fermions it is a vector-valued one. The collision terms of Boltzmann equations for fermions and bosons also possess the same general structure and differ only in the quantum effects associated with the final state of the reactions described. In particular, neutron-proton conversions in the early universe, which set the primordial Helium abundance, enjoy many similarities with Compton scattering which shapes the cosmic microwave background and we show that both can be handled with a Fokker-Planck type expansion. For neutron-proton conversions, this allows to obtain the finite nucleon mass corrections, required for precise theoretical predictions, whereas for Compton scattering it leads to the thermal and recoil effects which enter the Kompaneets equation. We generalize the latter to the general case of anisotropic and polarized photon distribution functions. Finally we discuss a parameterization of the photon spectrum based on logarithmic moments which allows for a neat separation between temperature shifts and spectral distortions.

中文翻译：

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宇宙学中相对论物种的辐射传输

我们回顾了费米子和玻色子（光子）气体分布函数的一般构造，强调了两种情况之间的异同。描述光子偏振的中心对象是张量值分布函数，而对于费米子，它是矢量值分布函数。费米子和玻色子的玻尔兹曼方程的碰撞项也具有相同的一般结构，不同之处仅在于与所描述反应的最终状态相关的量子效应。特别是，早期宇宙中的中子-质子转换，它设定了原始氦丰度，与康普顿散射有许多相似之处，康普顿散射塑造了宇宙微波背景，我们表明两者都可以用福克-普朗克型膨胀来处理。对于中子-质子转换，这允许获得精确理论预测所需的有限核子质量校正，而对于康普顿散射，它会导致进入 Kompaneets 方程的热和反冲效应。我们将后者推广到各向异性和偏振光子分布函数的一般情况。最后，我们讨论了基于对数矩的光子光谱参数化，它允许在温度偏移和光谱失真之间进行巧妙的分离。