Clifford代数的同位素提升及其在基本粒子质量矩阵中的应用
Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices
摘要：
研究了Clifford代数中代数结构的同位素提升问题，定义了一个新的乘积，它涉及Clifford代数中的一个任意但固定的元素。该元素作为引入产品的单位，称为isounit。我们在结合和非结合的任意代数中构造同位素，这些构造的例子使用Clifford代数展示，虽然结合，可以生成八元数，非结合，代数。整个形式主义是在Clifford代数舞台上发展起来的，也给出了引入外代数的同位素的必要前提。当构造了同位素李代数su（6）的生成元时，证明了u，d，s，c，b，t六夸克的味强子对称性是精确的，并证明了同位素Clifford代数的单位是六夸克质量的函数.约束参数的限制，即同位素群SU（6）中Isounit表示的条目，是基于最近对夸克质量施加的限制。
英文摘要：
Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra su(6) are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.
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