Minimal length uncertainty relation and ultraviolet regularization

1996/12/08 by Achim Kempf, A. Kempf, G. Mangano · 433 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Applied mathematics #Artificial intelligence #Computer science #Data mining #Mathematics #Optics #Physics #Regularization (linguistics) #Relation (database) #Scientific Measurement and Uncertainty Evaluation #Ultraviolet #gr-qc #hep-th #math-ph #math.MP #math.QA #q-alg #quant-ph

paper · pdf · doi:10.1103/physrevd.55.7909

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 55(12), 7909-7920 (American Physical Society) · 24 pages, LaTeX, 3 postscript figure files included via epsf option

arxiv created 1996/12/08 · openalex publication_date 1997/06/15 · arxiv updated 2010/11/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Studies in string theory and quantum gravity suggest the existence of a finite lower limit \ensuremathΔx₀ to the possible resolution of distances, at the latest on the scale of the Planck length of 10^\ensuremath-35 m. Within the framework of the Euclidean path integral we explicitly show ultraviolet regularization in field theory through this short distance structure. Both rotation and translation invariance can be preserved. An example is studied in detail.

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