The algebraic structure of the generalized uncertainty principle

1993/09/06 by Michele Maggiore · 52 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Mathematical and Theoretical Analysis #Noncommutative and Quantum Gravity Theories #hep-th

paper · pdf · doi:10.1016/0370-2693(93)90785-g

published as Phys.Lett. B319 (1993) 83-86 · 6 pages, IFUP-TH 38/93

arxiv created 1993/09/06 · openalex publication_date 1993/12/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter κ 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 Δp/M_{\rm PL}. We also briefly comment on possible implications for Lorentz invariance at the Planck scale.

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