Journal of Applied Mathematics and Physics

Volume 4, Issue 10 (October 2016)

ISSN Print: 2327-4352   ISSN Online: 2327-4379

Google-based Impact Factor: 0.63  Citations  

Generalized Uncertainty Relations, Curved Phase-Spaces and Quantum Gravity

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DOI: 10.4236/jamp.2016.410189    1,453 Downloads   2,008 Views   Citations


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.

Cite this paper

Castro, C. (2016) Generalized Uncertainty Relations, Curved Phase-Spaces and Quantum Gravity. Journal of Applied Mathematics and Physics, 4, 1870-1878. doi: 10.4236/jamp.2016.410189.

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