论文标题
在位置构造的海森堡代数的路径积分中，具有强量子重力测量
Path integral in position-deformed Heisenberg algebra with strong quantum gravitational measurement
论文作者
论文摘要
最近已被证明具有最大长度不确定性的位置的Heisenberg代数，可以在Planck量表（2022 J.Phys。A：Math。Theor.55105303）诱导强量子引力场。在本研究中，我们一方面使用位置空间表示形式，另一方面使用傅立叶变换及其反向表示来构建该变形代数内路径积分的传播器。讨论了自由粒子和简单的谐波振荡器的传播器和相应的动作作为示例。由于在这个欧几里得空间中量子重力的影响很强，因此我们表明描述了两种系统的经典轨迹的作用都受经典力学的普通轨迹界定。这表明量子重力弯曲了颗粒的路径，使它们可以从一个点迅速传播到另一个点。从数字上观察到经典作用值的降低，因为人们会增加量子重力效应。
Position-deformed Heisenberg algebra with maximal length uncertainty has recently been proven to induce strong quantum gravitational fields at the Planck scale (2022 J. Phys. A: Math. Theor.55 105303). In the present study, we use the position space representation on the one hand and the Fourier transform and its inverse representations on the other to construct propagators of path integrals within this deformed algebra. The propagators and the corresponding actions of a free particle and a simple harmonic oscillator are discussed as examples. Since the effects of quantum gravity are strong in this Euclidean space, we show that the actions which describe the classical trajectories of both systems are bounded by the ordinary ones of classical mechanics. This indicates that quantum gravity bends the paths of particles, allowing them to travel quickly from one point to another. It is numerically observed by the decrease in values of classical actions as one increases the quantum gravitational effects.
