论文标题
PQM与GUP：量子力学和宇宙学中晶格动力学和最小不确定性的含义
PQM and the GUP: Implications of Lattice Dynamics and Minimal Uncertainties in Quantum Mechanics and Cosmology
论文作者
论文摘要
我们比较了量子力学的两种替代表示：聚合物量子力学（PQM），其特征类似于环路量子重力和循环量子宇宙学，以及通用的不确定性原理（GUP）表示，通过修改的代数通过修改的代数产生与弦乐理论中的替代性不确定的原理相似的原理。这些形式主义可以重新铸造以显然相似，但是尽管GUP在位置上的绝对不确定性产生了绝对的不确定性，但PQM通过晶格实现某种紫外线截止，并且没有最小的不确定性。然后，我们在半经典级别上以类似Misner的变量的方式在各向异性的Bianchi I模型上实现它们：PQM始终意味着删除了奇异性，而GUP未能做到这一点，再次强调了这两个表示的基本上是不合时宜的。
We compare two alternative representations of quantum mechanics: Polymer Quantum Mechanics (PQM), which presents features similar to Loop Quantum Gravity and Loop Quantum Cosmology, and the Generalized Uncertainty Principle (GUP) representation, that through a modified Algebra yields an alternative uncertainty principle similar to those derived in String Theories and Brane Cosmology. These formalisms can be recast to apparently look similar, but while the GUP yields an absolute minimal uncertainty on position, PQM implements some kind of ultraviolet cut-off through a lattice and does not have a minimal uncertainty. Then we implement them on the anisotropic Bianchi I model in Misner-like variables on a semiclassical level: PQM always implies a removal of the singularities, while the GUP fails to do so, highlighting once again how the two representations are fundamentally incompatible.
