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Free, publicly-accessible full text available February 1, 2026
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Bhandari, Gaurav; Pathak, S D; Sharma, Manabendra; Wang, Anzhong (, arXivorg)The prediction of a minimal length scale by various quantum gravity candidates (such as string/M theory, Doubly Special Relativity, Loop Quantum Gravity and others) have suggested modification of Heisenberg Uncertainty Principle (HUP), resulting in the Generalized Uncertainty Principle (GUP). In this short review, we investigate the origins of the GUP and examine higher-order models, focusing on the linear plus quadratic form of the GUP. We extend the concept of minimal length to minimal angular resolution, which plays a crucial role in modifying angular momentum and its associated algebra. A comparison is made between the standard angular momentum commutator algebra and that modified by the GUP. Finally, we review its application in the hydrogen atom spectra and and discuss future endeavors.more » « lessFree, publicly-accessible full text available December 28, 2025
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Bhandari, Gaurav; Pathak, S D; Sharma, Manabendra; Wang, Anzhong (, General Relativity and Gravitation)
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Sharma, Manabendra; Vicente, Gustavo S; Graef, Leila L; Ramos, Rudnei O; Wang, Anzhong (, ArXiv)We consider a formulation of the Brans-Dicke theory in Jordan's frame for Bianchi-I spacetime within the framework of loop quantum gravity. The robustness of singularity resolutions due to the quantum effects is explicitly verified in the context of two quantization schemes typically used in the literature. We present an exploration of the effects of quantum geometry on the background dynamics, which is also illustrated through some explicit numerical examples and showing the absence of the singularity.more » « less
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