The gauge formalism in telepalallel gravity provides an interesting viewpoint to describe interactions according to an anholonomic observer’s tetrad basis. Without going into assessing the complete viability of quantization in an early stage, this paper explores classical gravity within the framework of a classical-to-quantum bridge between the SU(1, 3) Yang–Mills gauge formalism and the gauge-like treatment of teleparallel gravity. Specifically, the perturbed spacetime algebra with Weitzenböck connection can be assimilated to a local complexification based on the SU(1, 3) Yang–Mills theory, what we call hypercolor or, simply, color. The formulation of the hypercolor dynamics is build by a translational gauge, as in the teleparallel gravities. In particular, this work analyses small perturbations of a metric decomposition related to the Wilson line and the Kaluza–Klein metric, but obtaining electrodynamics in four dimensions. The spacetime coordinates are now matrices that represent elements of the \(\mathfrak {su}(1,3)\) algebra. To make compatible the formulation of a colored gravity with the Lorentz force and the Maxwell equations, it is enough to define every energy potential origin as 0 in the event horizon instead of the classic zero potential at infinity. Under the colored gravity framework, standard electromagnetism can be obtained as a particular abelian case.

Telepalallel Gravity 中的规范形式主义提供了一个有趣的观点，可以根据全基因组观察者的 tetrad 基来描述相互作用。本文没有在早期阶段评估量子化的完全可行性，而是在 SU（1， 3） Yang-Mills 规范形式和远平行引力的规范式处理之间的经典到量子桥梁的框架内探讨了经典引力。具体来说，具有 Weitzenböck 连接的扰动时空代数可以被同化为基于 SU（1， 3） Yang-Mills 理论的局部复杂化，我们称之为超色或简称为颜色。超色动力学的公式是由平移规范构建的，就像在遥平行引力中一样。特别是，这项工作分析了与 Wilson 线和 Kaluza-Klein 度量相关的度量分解的小扰动，但获得了四个维度的电动力学。时空坐标现在是表示 \（\mathfrak {su}（1,3）\） 代数元素的矩阵。为了使彩色引力的公式与洛伦兹力和麦克斯韦方程兼容，只需在事件视界中将每个能量势源定义为 0 而不是无穷远处的经典零势即可。在彩色引力框架下，标准电磁可以作为特定的阿贝尔情况获得。