Quantum Groups, Gravity, and the Generalized Uncertainty Principle

Details Quantum Groups, Gravity, and the Generalized Uncertainty Principle Quantum Groups, Gravity, and the Generalized Uncertainty Principle

1993-05-28

arxiv.org/abs/hep-th/9305163v3

Phys.Rev. D49 (1994) 5182-5187

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, IFUP-TH 19/93, May 1993 (revised Nov. 1993)

Scientific paper

10.1103/PhysRevD.49.5182

We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincar\'e algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial translations and rotations of the deformed Poincar\'e algebra obey a deformed Heisenberg algebra from which the generalized uncertainty principle follows. The result indicates that in the $\kappa$-deformed Poincar\'e algebra a minimal observable length emerges naturally.

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