arXiv 1801.025332018-01hep-thgr-qcquant-ph

非对易效应对流体动力学和Freidmann方程的修正

Noncommutative effects on the fluid dynamics and modifications of the Freidmann equation

Kai Ma

备注：: 19 pages; v2: title is changed, texts are improved, references are added

摘要：

本文提出了一种新的拉格朗日方法来研究非对易空间上的流体动力学。从单个粒子的泊松括号出发，考虑到非对易效应，构造了一个从正则拉格朗日变量到欧拉变量的映射。这种方法的优点是拉格朗日形式主义中的运动能和势能在无限极限内连续变化到欧拉形式主义中的运动能和势能，从而确保正确地考虑运动能和势能。此外，在我们的方法中，质量密度和电流密度的运动方程自然地表示为保守形式。在此基础上，引入非交换Poisson括号，得到了欧拉变量间的非交换代数，以及运动方程的非交换修正。我们发现，非对易修正一般依赖于所考虑的潜在的衍生物。此外，我们发现非对易代数确实修正了通常的Friedmann方程，并且非对易修正度量了密度函数$ρ(\vec{z})$在绕$\vecθ$方向旋转时的对称性.这种特性导致球对称质量密度分布和势的修正消失。

英文摘要：

We propose a new approach in Lagrangian formalism for studying the fluid dynamics on noncommutative space. Starting with the Poisson bracket for single particle, a map from canonical Lagrangian variables to Eulerian variables is constructed for taking into account of the noncommutative effects. The advantage of this approach is that the kinematic and potential energies in the Lagrangian formalism continuously change in the infinite limit to the ones in Eulerian formalism, and hence make sure that both the kinematical and potential energies are taken into account correctly. Furthermore, in our approach, the equations of motion of the mass density and current density are naturally expressed into conservative form. Based on this approach, the noncommutative Poisson bracket is introduced, and the noncommutative algebra among Eulerian variables, as well as the noncommutative corrections on the equations of motion are obtained. We find that the noncommutative corrections generally depend on the derivatives of potential under consideration. Furthermore, we find that the noncommutative algebra does modify the usual Friedmann equation, and the noncommutative corrections measure the symmetry properties of the density function $ρ(\vec{z})$ under rotation around the direction $\vecθ$. This characterization results in vanishing corrections for spherically symmetric mass density distribution and potential.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文