AI 中文总结
本文构造了在曲率参数α与非对易性参数β下均正则的Snyder-de Sitter代数的显式正则表示，该表示具有正确的平直、交换及标准相空间极限，可用于推导Snyder-de Sitter相空间的泊松规范变换，为相关物理系统研究提供便利框架。
AI 中文摘要
Snyder-de Sitter代数提供了相空间几何的洛伦兹协变形变，其特征为曲率参数α与非对易性参数β。我们构造了该代数的显式正则（Darboux）表示，该表示在两个参数下均为正则。从与Snyder-de Sitter泊松括号相关的辛结构出发，我们推导了物理相空间变量与Darboux坐标之间的正则变换，并以α和β的所有阶数得到其闭式逆变换。所得表示具有明确定义的平直极限（α→0）与交换极限（β→0），分别约化为Snyder相空间代数与de Sitter相空间代数，而同时取极限（α,β）→(0,0)则得到标准正则相空间坐标。随后，我们将该表示应用于Snyder-de Sitter相空间上泊松规范变换的构造，特别推导了对应的规范变换矩阵与泊松场强，二者在α和β下均为正则。我们的构造为研究基于Snyder-de Sitter相空间的规范理论及其他物理系统提供了便利框架。
英文摘要
The Snyder--de Sitter algebra provides a Lorentz-covariant deformation of phase-space geometry characterized by a curvature parameter $α$ and a noncommutativity parameter $β$. We construct an explicit canonical (Darboux) representation of this algebra that is regular in both parameters. Starting from the symplectic structure associated with the Snyder--de Sitter Poisson brackets, we derive the canonical transformation between the physical phase-space variables and Darboux coordinates and obtain its inverse in closed form to all orders in $α$ and $β$. The resulting representation has well-defined flat ($α\to0$) and commutative ($β\to0$) limits, reducing respectively to the Snyder and de Sitter phase-space algebras, while the simultaneous limit $(α,β)\to(0,0)$ yields the standard canonical phase-space coordinates. We then apply this representation to the construction of Poisson gauge transformations on Snyder--de Sitter phase space. In particular, we derive the corresponding gauge transformation matrix and Poisson field strength, both of which are regular in $α$ and $β$. Our construction provides a convenient framework for investigating gauge theories and other physical systems formulated on Snyder--de Sitter phase space.
Comments14 pages
