Generalized Uncertainty Relations, Curved Phase-Spaces and Quantum Gravity
Generalized Uncertainty Relations, Curved Phase-Spaces and Quantum Gravity作者机构：Quantum Gravity Research Topanga CA USA Center for Theoretical Studies of Physical Systems Atlanta USA Clark Atlanta University Atlanta GA USA
出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)
年 卷 期：2016年第4卷第10期
页 面：1870-1878页
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题：Uncertainty Relations Gravity Finsler Geometry Born Reciprocity Phase Space
摘 要：Modifications of the Weyl-Heisenberg algebra are proposed where the classical limit corresponds to a metric in (curved) momentum spaces. In the simplest scenario, the 2D de Sitter metric of constant curvature in momentum space furnishes a hierarchy of modified uncertainty relations leading to a minimum value for the position uncertainty . The first uncertainty relation of this hierarchy has the same functional form as the stringy modified uncertainty relation with a Planck scale minimum value for at . We proceed with a discussion of the most general curved phase space scenario (cotangent bundle of spacetime) and provide the noncommuting phase space coordinates algebra in terms of the symmetric and nonsymmetric metric components of a Hermitian complex metric , such . Yang’s noncommuting phase-space coordinates algebra, combined with the Schrodinger-Robertson inequalities involving angular momentum eigenstates, reveals how a quantized area operator in units of emerges like it occurs in Loop Quantum Gravity (LQG). Some final comments are made about Fedosov deformation quantization, Noncommutative and Nonassociative gravity.
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