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arXiv 2108.04322gr-qchep-th
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相对论广义不确定原理及其意义

Relativistic Generalized Uncertainty Principle and Its Implications

Vasil Todorinov

摘要:

对宇宙的基本物理描述基于两个理论:量子力学和广义相对论。量子引力(QG)的统一理论是一个悬而未决的问题。量子引力现象学(QGP)研究低能系统中的QG效应。一个这样的唯象模型的基础是广义不确定原理(GUP),这是一个修改后的海森堡不确定关系,并预测一个变形的位置-动量交换子。本文提出了相对论性广义不确定原理(RGUP),给出了一个Loerentz不变的最小长度,解决了合成律问题。给出了几个系统的RGUP修正Klein-Gordon、Schrodinger和Dirac方程,并给出了QG修正。得到了规范场、标量场和旋量场的量子电动力学的拉格朗日量。然后计算RGUP对散射振幅的修正。结果被应用到高能散射实验中,为实验室检验最小长度和QG理论提供了急需的窗口。

英文摘要:

The fundamental physical description of the Universe is based on two theories: Quantum Mechanics and General Relativity. Unified theory of Quantum Gravity (QG) is an open problem. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed position-momentum commutator. Relativistic Generalized Uncertainty Principle (RGUP) is proposed in this thesis, which gives a Loerentz invariant minimum length and resolves the composition law problem. RGUP modified Klein-Gordon, Schrodinger and Dirac equations with QG corrections to several systems are presented. The Lagrangians of Quantum Electrodynamics for the gauge, scalar, and spinor fields are obtained. The RGUP corrections to scattering amplitudes are then calculated. The results are applied to high energy scattering experiments providing much needed window for testing minimum length and QG theories in the laboratory.

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。

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