2018/01/08 by Kai Ma, Ma, Kai
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1801.02533
openalex publication_date 2018/01/08 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
We propose a new approach in Lagrangian formalism for studying the fluid\ndynamics on noncommutative space. Starting with the Poisson bracket for single\nparticle, a map from canonical Lagrangian variables to Eulerian variables is\nconstructed for taking into account of the noncommutative effects. The\nadvantage of this approach is that the kinematic and potential energies in the\nLagrangian formalism continuously change in the infinite limit to the ones in\nEulerian formalism, and hence make sure that both the kinematical and potential\nenergies are taken into account correctly. Furthermore, in our approach, the\nequations of motion of the mass density and current density are naturally\nexpressed into conservative form. Based on this approach, the noncommutative\nPoisson bracket is introduced, and the noncommutative algebra among Eulerian\nvariables, as well as the noncommutative corrections on the equations of motion\nare obtained. We find that the noncommutative corrections generally depend on\nthe derivatives of potential under consideration. Furthermore, we find that the\nnoncommutative algebra does modify the usual Friedmann equation, and the\nnoncommutative corrections measure the symmetry properties of the density\nfunction \ρ(\z) under rotation around the direction \\θ.\nThis characterization results in vanishing corrections for spherically\nsymmetric mass density distribution and potential.\n