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

Foundations of Physics 39 (5):510-518 (2009)

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→∞
Keywords Yang’s quantized space-time algebra (YSTA)  Inonu-Wigner contraction  Kinematical reduction of spatial degrees of freedom  Holographic relation in YSTA
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DOI 10.1007/s10701-008-9270-9
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