论文标题
广义不确定性原理中最小长度的微妙方面
A Subtle Aspect of Minimal Lengths in the Generalized Uncertainty Principle
论文作者
论文摘要
在这项工作中，我们指出了量化重力的普遍不确定性原理（GUP）方法的一个被忽视的和微妙的特征：即，具有相同修改的换向器的不同对经过的操作员，$ [\ hat {x}，\ hat {p} {p}] = i \ hbar（1+βp^2），可能没有所有物理$，例如所有物理上的后果。这些差异取决于位置和/或动量运算符的修改方式，而不仅仅是所得的修改后的换向器。在构建GUP模型时，这提供了指导，因为它区分了那些具有最小长度尺度的GUP，这是关于量子重力的一些广泛参数，而没有最小长度尺度的GUP。
In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator, $[\hat{X},\hat{P}] = i \hbar (1+βp^2)$, may have different physical consequences such as having no minimal length at all. These differences depend on how the position and/or momentum operators are modified rather than only on the resulting modified commutator. This provides guidance when constructing GUP models since it distinguishes those GUPs that have a minimal length scale, as suggested by some broad arguments about quantum gravity, versus GUPs without a minimal length scale.
