Contracted Representation of Yang's Spacetime Algebra and Buniy-Hsu-Zee's Discrete Spacetime
Tóm tắt
Motivated by the recent proposition by Buniy, Hsu, and Zee with respect to discrete spacetime and finite spatial degrees of freedom of our physical world with short- and long-distance scales, l
P
and L, we reconsider the Lorentz-covariant Yang's quantized spacetime algebra (YSTA), which is intrinsically equipped with two such 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 → ∓.
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