Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation
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 the noncommutative effects. The adv...
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Wiley
2018-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/6578204 |
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| author | Kai Ma |
| author_facet | Kai Ma |
| author_sort | Kai Ma |
| collection | DOAJ |
| description | 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 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 and 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(z→) under rotation around the direction θ→. This characterization results in vanishing corrections for spherically symmetric mass density distribution and potential. |
| format | Article |
| id | doaj-art-b1397e6dd8c74f13b886f1ccd1cfe517 |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-b1397e6dd8c74f13b886f1ccd1cfe5172025-02-03T01:01:38ZengWileyAdvances in High Energy Physics1687-73571687-73652018-01-01201810.1155/2018/65782046578204Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann EquationKai Ma0School of Physics Science, Shaanxi University of Technology, Hanzhong 723000, Shaanxi, ChinaWe 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 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 and 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(z→) under rotation around the direction θ→. This characterization results in vanishing corrections for spherically symmetric mass density distribution and potential.http://dx.doi.org/10.1155/2018/6578204 |
| spellingShingle | Kai Ma Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation Advances in High Energy Physics |
| title | Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation |
| title_full | Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation |
| title_fullStr | Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation |
| title_full_unstemmed | Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation |
| title_short | Noncommutative Effects on the Fluid Dynamics and Modifications of the Friedmann Equation |
| title_sort | noncommutative effects on the fluid dynamics and modifications of the friedmann equation |
| url | http://dx.doi.org/10.1155/2018/6578204 |
| work_keys_str_mv | AT kaima noncommutativeeffectsonthefluiddynamicsandmodificationsofthefriedmannequation |