论文标题
基于广义不确定性原理的非依赖性各向同性模型的框架
A framework for nonrelativistic isotropic models based on generalized uncertainty principles
论文作者
论文摘要
自然界中基本长度尺度的存在是不同量子重力模型的常见预测。可能会发现这种发现可能会深刻地改变量子现象的当前知识，并可能预期对海森堡的不确定性原则进行修改。尽管在过去几十年中对这种可能性的关注，但没有共同的框架来系统地研究所谓的普遍不确定性原则（GUP）。在这项工作中，我们在非同性量子力学的背景下提供了这样的框架。我们的方法基于很少的假设：基本的长度尺度，各向同性，均等和时间逆转转换的不变性以及位置和动量操作员的对称性。我们显示的简单维度分析允许建立一个统一的框架，其中包含各向同性的普遍不确定性原理（IGUP），并在详细介绍了框架的相关理论方面后，在这种情况下讨论了一些流行的GUP模型。最后，我们将经常研究的GUP模型的电流界限转化为此类IGUP框架参数的界限。
The existence of a fundamental length scale in Nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg uncertainty principle may be expected. Despite the attention given to this possibility in the past decades, there has been no common framework for a systematic investigation of so called generalized uncertainty principles (GUP). In this work we provide such framework in the context of nonrelativistic quantum mechanics. Our approach is based on very few assumptions: there is a fundamental length scale, space isotropy, invariance under parity and time reversal transformations, and symmetricity of the position and momentum operators. We show simple dimensional analysis allows for building a unified framework containing any isotropic generalized uncertainty principle (iGUP) and discuss some popular GUP models in this context after elaborating on relevant theoretical aspects of the framework. At last, we translate current bounds on three often investigated GUP models into bounds on parameters of such unified iGUP framework.
