The algebraic structure of the generalized uncertainty principle

Details The algebraic structure of the generalized uncertainty principle The algebraic structure of the generalized uncertainty principle

1993-09-06

arxiv.org/abs/hep-th/9309034v1

Phys.Lett. B319 (1993) 83-86

Physics

High Energy Physics

High Energy Physics - Theory

6 pages, IFUP-TH 38/93

Scientific paper

10.1016/0370-2693(93)90785-G

We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter $\kappa$ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at first order in $\Delta p/M_{\rm PL}$. We also briefly comment on possible implications for Lorentz invariance at the Planck scale.

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