Yang's Quantized Space-time Algebra and Holographic Hypothesis

Abstract

The present-day significance of Yang's quantized space-time algebra (YST) is pointed out from the holographic viewpoint. One finds that the D-dimensional YST and its modified version (MYST) have the background symmetry SO(D+1,1) and SO(D,2), which are well known to underlie the dS/CFT and AdS/CFT correspondences, respectively. This fact suggests a new possibility of dS/YST and AdS/MYST in parallel with dS/CFT and AdS/CFT, respectively. The spatial components of quantized space-time and momentum operators of YST have discrete eigenvalues and their respective minimums, $a$ and 1/R, without contradiction to Lorentz-covariance. With respect to MYST, the spatial components of space-time operators and the time component (energy) of momentum operators have discrete eigenvalues and their respective minimums, $a$ and 1/R, in contrast to YST. This discrete structure of YST and MYST, which CFT lacks entirely, may provide a theoretical ground for the unified regularization or cutoff of ultraviolet and infrared divergences familiar in the UV/IR connection in the holographic hypothesis.

13 pages

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• Conformal Vacua and Entropy in de Sitter Space
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• From Yukawa to M-Theory
• Where Does Black Hole Entropy Lie? Some Remarks on Area-Entropy Law, Holographic Principle and Noncommutative Space-Time
• Kinematical Holographic Relation in Yang's Quantized Space-Time and Area-Entropy Relation in $D_0$ Brane Gas System
• Free Massless Particles, Two Time Physics and Newtonian Gravitodynamics