标题： 由位置相关非对易性得出的极小和极大长度 显示英文标题

标题： Minimal and maximal lengths from position-dependent noncommutativity

摘要： 弗林格等人在题为“由位置依赖的非对易性引出的弦”的论文中，在二维空间引入了一组新的非对易空间对易关系。研究已表明，在这种空间-空间非对易性中引入的基本对象都是弦状的。考虑到这一结果，我们将弗林格等人的开创性工作推广到如下情形：除了位置依赖的非对易性外，还存在由海森堡不确定性关系的广义形式引出的最大长度和最小动量。最大长度的存在与粒子长度中额外的一阶项有关，这正是我们分析与他们不同的基本差异所在。这一最大长度解决了时空中的著名奇点问题。我们建立了这种非对易空间的不同表示形式，并最终利用这些新变量研究了一些基本且有趣的量子力学系统。 显示英文摘要

摘要： Fring and al in their paper entitled "Strings from position-dependent noncommutativity" have introduced a new set of noncommutative space commutation relations in two space dimensions. It had been shown that any fundamental objects introduced in this space-space non-commutativity are string-like. Taking this result into account, we generalize the seminal work of Fring and al to the case that there is also a maximal length from position-dependent noncommutativity and minimal momentum arising from generalized versions of Heisenberg's uncertainty relations. The existence of maximal length is related to the presence of an extra, first order term in particle's length that provides the basic difference of our analysis with theirs. This maximal length breaks up the well known singularity problem of space time. We establish different representations of this noncommutative space and finally we study some basic and interesting quantum mechanical systems in these new variables.