SU（2/1）超手征自对偶：描述电弱相互作用的一种新的量子、代数和几何范式
SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions
摘要：
本文将杨-米尔斯范式从李代数推广到内手征超代数。我们将李代数值联络单形$A$替换为一个混合了所有次外形并满足手征自对偶条件$\widetilde{A} = {}^*\widetilde{A} \,χ$的超代数值多形$\widetilde{A}$，其中$χ$表示超代数分次算子.这个超连接包含杨-米尔斯向量值在偶数李子代数，连同标量和自对偶张量值在奇数模，所有耦合只对电荷宇称CP-正费米子。费米子量子环然后诱导通常的杨-米尔斯-标量拉格朗日量，张量的自对偶Avdeev-Chizhov传播子，加上一个新的矢量-标量-张量顶点和几个四次项，这些项与超曲率的几何定义相匹配。应用于$SU(2/1)$ Lie-Kac简单超代数，它自然地分类所有的基本粒子，所得到的量子场论是无异常的，相互作用由超Killing度规和超代数的结构常数决定。
英文摘要：
We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form $A$, by a superalgebra-valued polyform $\widetilde{A}$ mixing exterior-forms of all degrees and satisfying the chiral self-duality condition $\widetilde{A} = {}^*\widetilde{A} \,χ$, where $χ$ denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. The Fermion quantum loops then induce the usual Yang-Mills-scalar Lagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a new vector-scalar-tensor vertex and several quartic terms which match the geometric definition of the supercurvature. Applied to the $SU(2/1)$ Lie-Kac simple superalgebra, which naturally classifies all the elementary particles, the resulting quantum field theory is anomaly-free and the interactions are governed by the super-Killing metric and by the structure constants of the superalgebra.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
