论文标题
能量截止，有效的理论，非交换性，模糊性：o（d） - 库态模糊球的情况
Energy cutoff, effective theories, noncommutativity, fuzzyness: the case of O(D)-covariant fuzzy spheres
论文作者
论文摘要
将量子理论投射到临界$ \叠加{e} $以下的国家的希尔伯特子空间上，可能会导致有效的理论，具有修改后的可观察结果，包括非共同空间（时间）。在原始空间的子曼福尔德$ n $上添加一个限制潜在的$ v $，最小值（时间）$ m $可能会导致$ n $的非交通量子理论的维度降低。 Here in particular we briefly report on our application of this procedure to spheres $S^d\subset\mathbb{R}^D$ of radius $r=1$ ($D=d\!+\!1>1$): making $\overline{E}$ and the depth of the well depend on (and diverge with) $Λ\in\mathbb{N}$ we obtain new fuzzy Spheres $ s^d_λ$ covariant在{\ it full}正交组$ o（d）$下方;坐标的换向因素仅取决于角动量，例如在Snyder非交通空间中。为了关注$ d = 1,2 $，我们还讨论了不确定性关系，国家的定位，太空坐标的对角和相干国家的建设。作为$λ\ to \ infty $ hilbert空间维度分歧，$ s^d_λ\ to s^d $，我们在$ s^d $上恢复了普通的量子力学。这些模型可能暗示了量子场理论，量子重力或凝结物理学的有效模型。
Projecting a quantum theory onto the Hilbert subspace of states with energies below a cutoff $\overline{E}$ may lead to an effective theory with modified observables, including a noncommutative space(time). Adding a confining potential well $V$ with a very sharp minimum on a submanifold $N$ of the original space(time) $M$ may induce a dimensional reduction to a noncommutative quantum theory on $N$. Here in particular we briefly report on our application of this procedure to spheres $S^d\subset\mathbb{R}^D$ of radius $r=1$ ($D=d\!+\!1>1$): making $\overline{E}$ and the depth of the well depend on (and diverge with) $Λ\in\mathbb{N}$ we obtain new fuzzy spheres $S^d_Λ$ covariant under the {\it full} orthogonal groups $O(D)$; the commutators of the coordinates depend only on the angular momentum, as in Snyder noncommutative spaces. Focusing on $d=1,2$, we also discuss uncertainty relations, localization of states, diagonalization of the space coordinates and construction of coherent states. As $Λ\to\infty$ the Hilbert space dimension diverges, $S^d_Λ\to S^d$, and we recover ordinary quantum mechanics on $S^d$. These models might be suggestive for effective models in quantum field theory, quantum gravity or condensed matter physics.
