Quantum Groups, Gravity, and the Generalized Uncertainty Principle

Preprint

3 November 1993

preprint
Published by arXiv in arXiv

Abstract

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.

Keywords

GENERALIZED UNCERTAINTY PRINCIPLE
UNCERTAINTY PRINCIPLE
DEFORMED POINCAR
QUANTUM GROUPS
GRAVITY
ALGEBRA
POINCAR

All Related Versions

Version 1, 1993-05-28, ArXiv
Version 2, 1993-11-03, ArXiv
Version 3, 1993-11-04, ArXiv
Published version: Physical Review D, 49 (10), 5182.

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