论文标题
是否存在特殊的相对论liouville方程？
Does A Special Relativistic Liouville Equation Exist?
论文作者
论文摘要
liouville方程是非相对论，非平衡经典统计力学的起点，由于两个问题，在特殊相对论中是有问题的。据称，相对论的哈密顿量不存在相互作用的粒子以及什么时间使用的问题，因为粒子都将有自己的时间作为时空坐标的一部分。在本文中，我研究了这个问题，令人惊讶地发现，在8n相空间中没有特殊的相对论liouville方程，其中n是粒子的数量，因为非相互作用和相互作用的粒子的规范性hamiltonian均为零。这是由于参数化对称性在定义了liouville方程演变的时间时，这会产生约束。这类似于以下事实：总的来说，该理论的一般相对性，差异性不变性始终给出零汉密尔顿式的，因为约束。
The Liouville Equation, the starting point of non-relativistic, non-equilibrium classical statistical mechanics, is problematic in special relativity because of two problems. A relativistic Hamiltonian is claimed not to exist for interacting particles and the problem of what time to use since the particles will all have their own time as part of their space-time coordinate. In this paper, I look at this problem and surprisingly found that there is no special relativistic Liouville equation in 8N phase space, where N is the number of particles, because the canonical Hamiltonian is zero for both non-interacting and interacting particles. This is due to the parametrization symmetry in defining a single time for the Liouville equation evolution, which results in a constraint.This is similar to the fact that in general relativity, diffeomorphism invariance of the theory always give a zero Hamiltonian because of a constraint.
