论文标题
标准模型，杰出的约旦代数和试验性
The Standard Model, The Exceptional Jordan Algebra, and Triality
论文作者
论文摘要
约旦，威格纳和冯·诺伊曼对量子机械可观察物的可能代数分类，发现它们属于4个“普通”家庭，再加上一个显着的离群：杰出的约旦代数。我们指出了该代数的络合力与粒子物理的标准模型之间的有趣关系，其最小的左右对称$ su（3）\ times su（2）_ {l} \ times su（2）_ {r} _ {r} \ times U（times times u（times times u（times time u（times u（Times times u））这表明了一种几何解释，其中一代标准模型费米子由切线空间$（\ Mathbb {C} \ otimes \ Mathbb {o}）^{2} $的单位射击射击平面^{2} $描述。
Jordan, Wigner and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 "ordinary" families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing relationship between the complexification of this algebra and the standard model of particle physics, its minimal left-right-symmetric $SU(3)\times SU(2)_{L}\times SU(2)_{R}\times U(1)$ extension, and $Spin(10)$ unification. This suggests a geometric interpretation, where a single generation of standard model fermions is described by the tangent space $(\mathbb{C}\otimes\mathbb{O})^{2}$ of the complex octonionic projective plane, and the existence of three generations is related to $SO(8)$ triality.
