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

TL;DR

This paper explores how Yang's quantized space-time algebra inherently limits spatial degrees of freedom, providing a kinematical basis for the holographic principle and potentially leading to divergence-free quantum field theories.

Contribution

It demonstrates that YSTA naturally reduces spatial degrees of freedom and establishes a kinematical holographic relation as a foundational aspect of quantum theory.

Findings

YSTA yields a finite number of degrees of freedom in bounded regions.

A kinematical holographic relation is derived within YSTA.

The relation suggests a primordial form of the holographic principle.

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, $\lambda$ 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, $\lambda \to 0$ and $R \to \infty.$