Contracted Representation of Yang's Space-Time Algebra and Buniy-Hsu-Zee's Discrete Space-Time

Abstract

Motivated by the recent proposition by Buniy, Hsu and Zee with respect to discrete space-time and finite spatial degrees of freedom of our physical world with a short- and a long-distance scales, $l_P$ and $L,$ we reconsider the Lorentz-covariant Yang's quantized space-time algebra (YSTA), which is intrinsically equipped with such two kinds of scale parameters, $\lambda$ and $R$. In accordance with their proposition, we find the so-called contracted representation of YSTA with finite spatial degrees of freedom associated with the ratio $R/\lambda$, which gives a possibility of the divergence-free noncommutative field theory on YSTA. The canonical commutation relations familiar in the ordinary quantum mechanics appear as the cooperative Inonu-Wigner's contraction limit of YSTA, $\lambda \to 0$ and $R\to \infty .$

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Cited by in corpus (4)

• A Short Essay on Quantum Black Holes and Underlying Noncommutative Quantized Space-Time
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• Holographic Relation in Yang's Quantized Space-Time Algebra and Area-Entropy Relation in $D_0$ Brane Gas System. II
• Kinematical Holographic Relation in Yang's Quantized Space-Time and Area-Entropy Relation in $D_0$ Brane Gas System