标题： 内含的超代数：最轻的标准模型粒子表示形成一个$\mathbb{Z}_2^5$-分级代数 显示英文标题

标题： A Superalgebra Within: representations of lightest standard model particles form a $\mathbb{Z}_2^5$-graded algebra

摘要： 研究展示了标准模型中一组熟悉的粒子表示如何共同构成一个超代数。 那些反映标准模型规范玻色子行为以及三代费米子的表示都包含在这个代数中，唯独不包括涉及顶夸克的不可约表示（irreps）。 这个超代数同由除法代数生成的 $16\times 16$ 埃氏矩阵的欧几里得若尔当代数是同构的， $H_{16}(\mathbb{C}),$ 并且通过除法代数生成。 这种除法代数的子结构允许在内禀对称性和时空对称性之间进行自然分解。 此外，它还允许在代数上定义一个 $\mathbb{Z}_2^5$ 次分次。 那些符合这种子结构的内禀对称性被发现是 $\mathfrak{su}(3)_C \oplus \mathfrak{su}(2)_L \oplus \mathfrak{u}(1)_Y,$，外加四次迭代的 $\mathfrak{u}(1)$。 对于空间对称性，可以找到多个 $\mathfrak{so}(3)$ 的副本。 鉴于其若尔当代数基础及其明显的非相对论特性，该模型可能在粒子物理和量子计算之间架起一座桥梁。 显示英文摘要

摘要： It is demonstrated how a set of particle representations, familiar from the Standard Model, collectively form a superalgebra. Those representations mirroring the behaviour of the Standard Model's gauge bosons, and three generations of fermions, are each included in this algebra, with exception only to those irreps involving the top quark. This superalgebra is isomorphic to the Euclidean Jordan algebra of $16\times 16$ hermitian matrices, $H_{16}(\mathbb{C}),$ and is generated by division algebras. The division algebraic substructure enables a natural factorization between internal and spacetime symmetries. It also allows for the definition of a $\mathbb{Z}_2^5$ grading on the algebra. Those internal symmetries respecting this substructure are found to be $\mathfrak{su}(3)_C \oplus \mathfrak{su}(2)_L \oplus \mathfrak{u}(1)_Y,$ in addition to four iterations of $\mathfrak{u}(1)$. For spatial symmetries, one finds multiple copies of $\mathfrak{so}(3)$. Given its Jordan algebraic foundation, and its apparent non-relativistic character, the model may supply a bridge between particle physics and quantum computation.