论文标题
部分可观测时空混沌系统的无模型预测
A Lagrangian with $E_8\times E_8$ symmetry for the standard model and pre-gravitation I. -- The bosonic Lagrangian, and a theoretical derivation of the weak mixing angle
论文作者
论文摘要
在较早的工作的基础上，我们提出了一个基本的拉格朗日语，用于将标准模型与预授权统一，并假定具有不间断的$ e_8 \ times e_8 $对称性。 Lagrangian是按照牛顿动力学中自由粒子的动能进行了图案的，将其概括为在分裂的生物涂片空间上的2-Brane的基质值Lagrangian动力学。对称破裂产生了三代人的标准模型夸克和叶子，以及已知的量规交互，以及一种新颖的右手$ su（3）_ {aver} \ times su（2）_r \ times _g \ times u（1）_g $确定为预雷德。本系列论文的目的是研究这种前量子前的矩阵矩阵值的拉格朗日动力学是否会导致标准模型的量子场理论的出现以及经典的一般相对性，可能会带有一些其他校正。在本文中，我们研究了拉格朗日人的骨髓部分，并展示了如何从小学拉格朗日式中回收预期的32个轨迹玻色子。作为应用程序，我们表明，渐近低能弱混合角$θ_W$由方程的解决方案$ 1 =（1/2）\ sqrt {\ cos（θ_{w}/2）}+ \ sqrt {\ sin（θ_{th）
Building on earlier work, we propose an elementary Lagrangian for the unification of the standard model with pre-gravitation, assumed to have an unbroken $E_8 \times E_8$ symmetry. The Lagrangian is patterned after the kinetic energy of a free particle in Newtonian dynamics, generalising it to the matrix-valued Lagrangian dynamics of a 2-brane on a split bioctonionic space. Symmetry breaking gives rise to the standard model quarks and leptons of three generations along with the known gauge interactions, and a novel right-handed counterpart $SU(3)_{grav}\times SU(2)_R \times U(1)_g$ identified as pre-gravitation. The goal of the present series of papers is to investigate if this pre-quantum, pre-spacetime matrix-valued Lagrangian dynamics can lead to the emergence of quantum field theory for the standard model, and classical general relativity, possibly with some additional corrections. In this paper we work out the bosonic part of the Lagrangian, and show how the anticipated 32 gauge bosons are recovered from the elementary Lagrangian. As an application, we show that the asymptotic low energy weak mixing angle $θ_W$ is given by a solution of the equation $1 = (1/2)\sqrt{ \cos(θ_{W}/2)}+ \sqrt {\sin(θ_{W}/2)}$, yielding $\sin^2θ_W \approx 0.24996$.
