广义不确定原理的相对定域性和相对共域性
Relative locality and relative Co-locality as extensions of the Generalized Uncertainty Principle
摘要：
我介绍的相对定域性的形式主义内的空间曲率效应作为一个非交换结构的动量空间与量子群的非常著名的概念。这给出了一个自然的红移效应，符合广义不确定原理（GUP）的扩展版本，也符合广义相对论中曲率的标准概念。然后，我介绍了相对共定域的概念，作为对通常的时空曲率概念的重新解释。从这个重新定义，我得到的动量空间曲率效应作为一个非交换性的位置空间。这引入了与GUP的扩展版本一致的自然蓝移效应。在量子群$SU_q(n)$对称Heisenberg代数及其q-Bargmann Fock表示的形式体系中，相对定域性和共定域性是相互对偶的.当引入相对定域性和协同定域性时，q变形参数的形式为$q\approx 1+\sqrt{\frac{\vert p\vert \vert x\vert}{r_Λm_{pl}}}$，其中相对定域性中的空间曲率效应表现为$ΔX\approx \frac{\vert x\vert}{m_{pl}}ΔP$，相对协同定域性中的动量曲率效应表现为$ΔP\approx \frac{\vert p\vert}{r_Λ}ΔX$，其中$r_Λ=\frac{1}{\sqrtΛ}$是由宇宙学常数定义的尺度$Λ$，$m_{pl}$是普朗克质量，$ΔX/ΔP$是与事件相关的位置/动量或时间/能量的尺度，p和x是观察者相对于事件的动量和位置。
英文摘要：
I introduce the spatial curvature effects inside the formalism of Relative Locality as a non-commutative structure of the momentum space in agreement with the very well known concepts of Quantum Groups. This gives a natural red-shift effect in agreement with an extended version of the Generalized Uncertainty Principle (GUP) and in agreement with the standard notions of curvature inside General Relativity. I then introduce the concept of Relative Co-locality as a reinterpretation of the usual notions of spacetime curvature. From this redefinition, I obtain the momentum space curvature effects as a non-commutativity in position space. This introduce a natural blue-shift effect in agreement with the extended version of GUP. Both effects, Relative locality and Co-locality are dual each other inside the formalism of quantum groups $SU_q(n)$ symmetric Heisenberg algebras and their q-Bargmann Fock representations. When Relative locality and Co-locality are introduced, the q-deformation parameter takes the form $q\approx 1+\sqrt{\frac{\vert p\vert \vert x\vert}{r_Λm_{pl}}}$ with the spatial curvature effects in Relative Locality appearing like $ΔX\approx \frac{\vert x\vert}{m_{pl}}ΔP$ and the momentum curvature effects in Relative Co-locality appearing like $ΔP\approx \frac{\vert p\vert}{r_Λ}ΔX$, where $r_Λ=\frac{1}{\sqrtΛ}$ is the scale defined by the Cosmological Constant $Λ$, $m_{pl}$ is the Planck mass and $ΔX/ΔP$ is a scale of position/momentum or time/energy associated with the event, p and x are the momentum and position of the observer relative to the event.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
