Moyal非交换框架中的相坐标变换、二维谐振子与Painlevé第二方程

中文摘要 AI 辅助

本工作旨在探索Moyal非交换形式论的物理应用，通过引入新的变换，这些变换借助描述Moyal非交换形变的参数，将旧的正则坐标连接到纯非交换的相坐标。这些变换与Moyal非交换括号一致，并构建了十六分量的无迹反对称张量。该形式论包含了空间-空间和空间-动量非交换性，而非仅限于正则坐标的非交换性（海森堡量子对易）。这些变换被用于构造二维谐振子的非交换类比及其超可积性，以及Painlevé第二方程。相关的形变哈密顿量还涉及一些额外的对称性，并揭示了对附加对称性与非交换结构之间关系的深层物理理解。Painlevé第二非交换坐标变换也被有效应用于生成第一个Yablonskii-Vorobev多项式，并伴随Painlevé第二参数变换。

英文摘要

This work aims to explore the physical application of Moyal noncom- mutative formalism with the the presentation of new transformations which connect the old canonical coordinates to purly noncommuting phase coordi- nates through the parameters describe the Moyal noncommutative deforma- tion. These transformations are consistent with the Moyal noncommunica- tive brackets and build sixteen components traceless anti-symmetric tensor. This formalism incorporates space-space and space-momentum noncommu- taivity rather then noncommutativity (Heisenberg quantum commutation ) only for the canonical coordinates. The transformations imply to construct noncommutative analogs of 2-dimensional harmonic oscillator with its superintegrability and Painlevé second equation. The associated deformed Hamiltonians additionally involve some extra symmetries and reveal a deep physical understanding of about the additional symmetries with noncommunicative structure. The Painlevé second noncommutative coordinates transformation are also efficiently applied to generate the first Yablonskii Vorobev polynomial with Painlevé second parameter transformation.

发表机构

• Center for High Energy Physics, University of the Punjab（旁遮普大学高能物理中心）

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