论文标题
GUP的新的非交通和较高衍生品量子力学
New Non-commutative and Higher Derivatives Quantum Mechanics from GUPs
论文作者
论文摘要
我们探索了一类新的非线性GUP（NLGUP），显示了一种新的非交通和较高衍生物量子力学的出现。在其中，我们将最短的基本量表作为NLGUP换向器中的紫外线固定点[X，P] = I \ HBAR F（P）中引入，牢记了与Planck量表相关的基本最高能量阈值。我们表明，这会导致空间坐标的换向性，这开始取决于系统的角动量。另一方面，非线性GUP必须将Schrodinger方程重新定义为新的非本地积分分化方程。我们还讨论了时间依赖性的扰动方法的戴森系列的修改。这可能表明，在NLGUP中，非交换性和较高的衍生物可能在统一和连贯的代数中密切相关。我们还表明，根据NLGUP，Dirac和Klein-Gordon方程的扩展为更高的空间衍生物。我们对分散速度计算量依赖于动量的校正，表明洛伦兹的不变性已变形。我们对伽马射线或大麻的光分散关系测试的可能含义发表评论，并具有潜在的利益，例如Lhaaso，Hawc和CTA等实验。
We explore a new class of Non-linear GUPs (NLGUP) showing the emergence of a new non-commutative and higher derivatives quantum mechanics. Within it, we introduce the shortest fundamental scale as a UV fixed point in the NLGUP commutators [X, P] = i\hbar f(P), having in mind a fundamental highest energy threshold related to the Planck scale. We show that this leads to lose commutativity of space coordinates, that start to be dependent by the angular momenta of the system. On the other hand, non-linear GUP must lead to a redefinition of the Schrodinger equation to a new non-local integral-differential equation. We also discuss the modification of the Dyson series in time-dependent perturbative approaches. This may suggest that, in NLGUPs, non-commutativity and higher derivatives may be intimately interconnected within a unified and coherent algebra. We also show that Dirac and Klein-Gordon equations are extended with higher space-derivatives according to the NLGUP. We compute momenta-dependent corrections to the dispersion velocity, showing that the Lorentz invariance is deformed. We comment on possible implications in tests of light dispersion relations from Gamma-Ray-Bursts or Blazars, with potential interests for future experiments such as LHAASO, HAWC and CTA.
