论文标题
GUP在强力场中的空间离散性
Discreteness of Space from GUP in Strong Gravitational Fields
论文作者
论文摘要
大量的重力理论表明，海森堡的不确定性原理被修改为普朗克量表附近的“广义不确定性原理”（GUP）。还已经显示，GUP甚至在低能量下也会引起所有量子机械汉密尔顿人的扰动校正，从而引入了Schrödinger方程和相对论量子机械方程的Planck量表校正。这些校正中的一些会导致低能实验室的潜在可测量作用。这些校正的另一个预测是，必须在一个，二维和三维框中研究GUP修改后的Schrödinger，Klein-Gordon和Dirac方程的解决方案，从而可以量化测得的长度。随后将该结果扩展到重力较弱的空间。在这项工作中，我们将此长度的量化进一步扩展到具有强力磁场的空间，并表明该结果继续存在，从而表明它是坚固的。
A large class of quantum theories of gravity show that the Heisenberg's uncertainty principle is modified to the "Generalised Uncertainty Principle" (GUP) near the Planckian scale. It has also been shown that the GUP induces perturbative corrections to all quantum mechanical Hamiltonians, even at low energies, and thereby introduces Planck scale corrections to the Schrödinger equation and to the relativistic quantum mechanical equations. Some of these corrections give rise to potentially measurable effects in the low-energy laboratory. Another prediction of these corrections is that a measured length must be quantized, as seen by studying the solutions of the GUP modified Schrödinger, Klein-Gordon, and Dirac equations in a one, two, and three dimensional box. This result was subsequently extended to spacetimes with weak gravitational fields. In this work, we further extend this length quantization to spacetimes with strong gravitational fields and show that this result continues to hold, thereby showing that it is robust.
