论文标题
离散缸的积分量化
Integral Quantization for the Discrete Cylinder
论文作者
论文摘要
协变量的积分量化是基于通过归一化正运算符的连续或离散族的认同措施（POVM）解决身份的，它们具有吸引人的概率含量，并且以协变量的方式转换。他们的优势之一是由于经典模型中存在奇异性而避免问题。在本文中，我们为相位空间为$ \ mathbb {z} \ times \，\ mathbb {s}^1 $（即，对于在圆圈移动的系统）的系统中实现了协变量量化。该相空间的对称组是Weyl-Heisenberg组的离散\＆Compact版本，即Abelian Group $ \ Mathbb {Z} \ Times \，\ Mathrm {so}（so}（2）$的中心扩展。在这方面，相位空间被视为该组的正确固定位置。该组的非平凡的统一不可约的表示，因为在$ l^2（\ mathbb {s}^1）$上作用于相位空间上是正方形的。我们展示了如何从相位空间上的（权重）函数（以及结果分辨率的分辨率}中得出相应的协变量量化}。 {作为后者的特殊情况}，我们用debièvre-del olmo-gonzales和kowalski-rembielevski-papaloucas在圆圈上恢复了量化。我们方法的另一个直接结果是Mukunda Wigner变换。我们还研究了由转移的高斯人，冯·米塞斯（Von Mises），泊松（Poisson）和fejér内核（FejérNecnels）建立的连贯国家的具体案例。在恒星表示中的申请正在进行中。
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalised positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a covariant way. One of their advantages is to allow to circumvent problems due to the presence of singularities in the classical models. In this paper we implement covariant integral quantizations for systems whose phase space is $\mathbb{Z}\times\,\mathbb{S}^1$, i.e., for systems moving on the circle. The symmetry group of this phase space is the discrete \& compact version of the Weyl-Heisenberg group, namely the central extension of the abelian group $\mathbb{Z}\times\,\mathrm{SO}(2)$. In this regard, the phase space is viewed as the right coset of the group with its center. The non-trivial unitary irreducible representation of this group, as acting on $L^2(\mathbb{S}^1)$, is square integrable on the phase space. We show how to derive corresponding covariant integral quantizations from (weight) functions on the phase space {and resulting resolution of the identity}. {As particular cases of the latter} we recover quantizations with de Bièvre-del Olmo-Gonzales and Kowalski-Rembielevski-Papaloucas coherent states on the circle. Another straightforward outcome of our approach is the Mukunda Wigner transform. We also look at the specific cases of coherent states built from shifted gaussians, Von Mises, Poisson, and Fejér kernels. Applications to stellar representations are in progress.
