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

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 shortand a long-distance scales, lP 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, λ 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/λ, 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, λ → 0 and R → ∞. ——————————————————