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Kinematical Reduction of Spatial Degrees of Freedom and Holographic Relation in Yang’s Quantized Space-Time Algebra

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Abstract

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞.

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  1. Kurodani 33-4, Sakyo-ku, Kyoto, 606-8331, Japan

    Sho Tanaka

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  1. Sho Tanaka
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Correspondence to Sho Tanaka.

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S. Tanaka is an Em. Professor of Kyoto University.

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Tanaka, S. Kinematical Reduction of Spatial Degrees of Freedom and Holographic Relation in Yang’s Quantized Space-Time Algebra. Found Phys 39, 510–518 (2009). https://doi.org/10.1007/s10701-008-9270-9

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  • DOI: https://doi.org/10.1007/s10701-008-9270-9

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