量子场论中的Boltzmann方程
The Boltzmann Equation from Quantum Field Theory
摘要：
我们从第一性原理表明经典玻尔兹曼方程的出现，从相对论非平衡量子场论所描述的Kadanoff-Baym方程。我们的方法适用于一个通用的量子场，耦合到收集的背景场和源，在一个均匀和各向同性的时空。分析是基于完整的Kadanoff-Baym方程的解析解，使用WKB近似。这与以前的动力学方程推导相反，以前的动力学方程推导依赖于类似的物理假设，但从动量空间中的梯度展开获得近似的运动方程。我们表明，系统遵循广义玻尔兹曼方程时，WKB近似举行。广义玻尔兹曼方程，其中包括离壳输运，是有效的远离平衡和时间依赖的背景下，如膨胀的宇宙。
英文摘要：
We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff-Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff-Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.
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