论文标题
夸克系统的符号信件
On symbol correspondences for quark systems
论文作者
论文摘要
我们介绍了在$ su（3）$下为对称的机械系统的符号对应的表征，我们称为夸克系统。量子系统是$ su（3）$的单一不可约的表示，由$ q（p，q）$，$ p，q \ in \ mathbb n_0 $以及其运营商代数表示。我们研究了经典相位空间是一个共同连接轨道的案例：复杂的投影平面$ \ MATHBB CP^2 $或FLAM歧管是光纤束$ \ MATHBB CP^1 \ jkingrightArrow \ Mathcal e \ to \ Mathbb cp^2 $。在第一种情况下，我们指的是纯夸克系统，其对应关系的表征是根据特征数字给出的，类似于旋转系统的情况，请参见。 [24]。在第二种情况下，我们指的是通用夸克系统，其对应关系的表征是根据特征矩阵给出的，该矩阵引入了各种新颖的特征。此外，对于纯夸克系统，我们介绍了量子运算符及其相应的经典功能扭曲产品的$ SU（3）$分解。为了准备对这些扭曲产品的渐近分析，我们还提出了经典功能的点式产物的$ SU（3）$分解。
We present the characterization of symbol correspondences for mechanical systems that are symmetric under $SU(3)$, which we refer to as quark systems. The quantum systems are the unitary irreducible representations of $SU(3)$, denoted by $Q(p,q)$, $p,q\in\mathbb N_0$, together with their operator algebras. We study the cases when the classical phase space is a coadjoint orbit: either the complex projective plane $\mathbb CP^2$ or the flag manifold that is the total space of fiber bundle $\mathbb CP^1\hookrightarrow \mathcal E\to \mathbb CP^2$. In the first case, we refer to pure-quark systems and the characterization of their correspondences is given in terms of characteristic numbers, similarly to the case of spin systems, cf. [24]. In the second case, we refer to generic quark systems and the characterization of their correspondences is given in terms of characteristic matrices, which introduces various novel features. Furthermore, we present the $SU(3)$ decomposition of the product of quantum operators and their corresponding twisted products of classical functions, for both pure and generic quark systems. In preparation for asymptotic analysis of these twisted products, we also present the $SU(3)$ decomposition of the pointwise product of classical functions.
