Liouville equations for neutrino distribution matrices
Liouville equations for neutrino distribution matrices
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中微子分布矩阵的刘维尔方程
DOI：
10.1103/physrevd.78.085017
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发表时间：
2007
影响因子：
5
通讯作者：
C. Cardall
中科院分区：
文献类型：
--
作者：
C. Cardall
单粒子标量分布函数或相空间密度的经典概念可以推广到矩阵，以适应离散量子数的叠加态，如中微子质量/味道。这样的“中微子分布矩阵”是一个合适的结构来描述中微子气体，它可以在空间和时间上变化，并且其中味道混合与碰撞竞争。相对论性中微子分布矩阵所服从的刘维尔方程，包括空间导数和真空味混合项，可以用两种新的方法明确而优雅地导出：从熟悉的简单味混合模型的协变版本，以及从量子“密度函数”（成对量子场算符的平均值）所满足的克莱因-戈登方程。与后一种推导相关的是一个案例研究，研究经典气体（尽管有费米统计）的联合位置/动量依赖性如何从建立在量子场上的形式主义中出现。
The classical notion of a single-particle scalar distribution function or phase space density can be generalized to a matrix in order to accommodate superpositions of states of discrete quantum numbers, such as neutrino mass/flavor. Such a "neutrino distribution matrix" is thus an appropriate construct to describe a neutrino gas that may vary in space as well as time and in which flavor mixing competes with collisions. The Liouville equations obeyed by relativistic neutrino distribution matrices, including the spatial derivative and vacuum flavor mixing terms, can be explicitly but elegantly derived in two new ways: from a covariant version of the familiar simple model of flavor mixing, and from the Klein-Gordon equations satisfied by a quantum "density function" (mean value of paired quantum field operators). Associated with the latter derivation is a case study in how the joint position/momentum dependence of a classical gas (albeit with Fermi statistics) emerges from a formalism built on quantum fields.