新相对论的现状与纲领
The status and programs of the New Relativity Theory
摘要：
本文综述了新相对论的最新成果。其中包括黑洞熵面积关系及其$logarithmic$修正的直接推导;弦不确定关系的推导和推广;四维引力共形异常与精细结构常数之间的关系;非对易几何、负概率和Cantorian分形时空在杨氏双缝实验中的作用。然后，我们将最近在$D$维中构造的淬灭超小空间玻色子$p$ -膜传播子（$AACS$ [18]）推广到包含所有$p$ -膜的全多维情形：在与生活在目标$D$ -昏暗背景时空中的$p$ -圈历史的嵌套族相关联的Clifford空间（$C$ -空间）中构造多维粒子传播子。我们展示了如何有效的$C$空间几何关系到普通时空的$extrinsic$曲率。研究了刚性粒子/膜的运动，以解释经典自旋的自然$emergence$。讨论了$C$ -空间几何与${\cal W}$、Finsler几何与（辫）量子群之间的关系.最后对$C$ -空间几何的黎曼长距离极限作了一些评述。
英文摘要：
A review of the most recent results of the New Relativity Theory is presented. These include a straightforward derivation of the Black Hole Entropy-Area relation and its $logarithmic$ corrections; the derivation of the string uncertainty relations and generalizations ; ; the relation between the four dimensional gravitational conformal anomaly and the fine structure constant; the role of Noncommutative Geometry, Negative Probabilities and Cantorian-Fractal spacetime in the Young's two-slit experiment. We then generalize the recent construction of the Quenched-Minisuperspace bosonic $p$-brane propagator in $D$ dimensions ($AACS$ [18]) to the full multidimensional case involving all $p$-branes : the construction of the Multidimensional-Particle propagator in Clifford spaces ($C$-spaces) associated with a nested family of $p$-loop histories living in a target $D$-dim background spacetime . We show how the effective $C$-space geometry is related to $extrinsic$ curvature of ordinary spacetime. The motion of rigid particles/branes is studied to explain the natural $emergence$ of classical spin. The relation among $C$-space geometry and ${\cal W}$, Finsler Geometry and (Braided) Quantum Groups is discussed. Some final remarks about the Riemannian long distance limit of $C$-space geometry are made.
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