论文标题
建立基于切线束的基本几何结构的基本物理相互作用的统一理论
Towards a unified theory of the fundamental physical interactions based on the underlying geometric structure of the tangent bundle
论文作者
论文摘要
本文提出了这样一个假设，即SO（3,1）组的中心延伸小组的切线束（TB）作为量规组是基本物理相互作用的统一理论的基本几何结构。基于这一假设作为最近的第一步，我提出了一种广义的电子相互作用理论，其中包括假设的暗物质颗粒（Eur。phys。Jc 79，779，779（2019）。切线束的垂直拉普拉斯具有与2d半数量子hall系统的Hamiltonian相同的形式。在TB中显示出SU（3）的颜色对称性，这是一种与Chern-Simon仪表相似的对称性，这预测了Quark consections Quark consements的通用大规模限制在平均场近似值中计算夸克式的配对，该近似允许对真空的特征参数（例如其化学势）的数值估计，Quark凝结参数和真空能量以前注意到对重力的理论理解是通过考虑到TBERTEM TB（3，因此均为TB）的理论。已知的基本相互作用与物理的几何化计划有关。
This paper pursues the hypothesis that the tangent bundle (TB) with the central extended little groups of the SO(3,1) group as gauge group is the underlying geometric structure for a unified theory of the fundamental physical interactions. Based on this hypothesis as a first step recently I presented a generalized theory of electroweak interaction which includes hypothetical dark matter particles (Eur. Phys. J C 79, 779 (2019). The vertical Laplacian of the tangent bundle possesses the same form as the Hamiltonian of a 2D semiconductor quantum Hall system. This explains fractional charge quantization of quarks and the existence of lepton and quark families. As will be shown the SU(3) colour symmetry for strong interaction arises in the TB as an emergent symmetry similar as Chern-Simon gauge symmetries in quantum Hall systems. This predicts a signature of quark confinement as an universal large-scale property of the Chern-Simon fields and induces a new understanding of the vacuum as the ground state occupied with a condensate of quark-antiquark pairs. The gap for quark-antiquark pairing is calculated in the mean-field approximation which allows a numerical estimation of the characteristic parameters of the vacuum such as its chemical potential, the quark condensation parameter and the vacuum energy. Note that previously a gauge theoretical understanding of gravity has been achieved by considering the translation group T(3,1) in the TB as gauge group. Therefore the theory presented here can be considered as a new type of unified theory for all known fundamental interactions linked with the geometrization program of physics.
