论文标题
$ \ mathbb {z} _2^2 $ - 级别$ {\ cal n} = 2 $ supersymmetry algebra和$ \ mathbb {z} _2^2 $ graded supermegryics
Irreducible representations of $\mathbb{Z}_2^2$-graded ${\cal N} =2$ supersymmetry algebra and $\mathbb{Z}_2^2$-graded supermechanics
论文作者
论文摘要
$ \ mathbb {z} _2^2 $降级的超对称代数的$ {\ cal n} = 2 $的不可约的表示（IRRERP）是通过诱导的代表来获得的，它们可用于导出$ \ \ Mathbb {Z} _2^2 $ graded supersymmpermmmetricmmmetricm metsical compantical。 $λ= 0 $的列表是四个维度，其中$λ$是Casimir元素的特征值，而$λ\ neq 0的八维为八维。缩小的四个维度列表用于定义$ \ mathbb {z} _2^2 $降级的超对称转换，并在转换下不变下不变。结果表明，如果特定$ \ mathbb {z} _2^2 $ -Degree的所有变量都是辅助的，则NOETHE费用之一就会消失。
Irreducible representations (irreps) of $\mathbb{Z}_2^2$-graded supersymmetry algebra of ${\cal N}=2$ are obtained by the method of induced representation and they are used to derive $\mathbb{Z}_2^2$-graded supersymmetric classical actions. The irreps are four dimensional for $ λ= 0$ where $ λ$ is an eigenvalue of the Casimir element, and eight dimensional for $λ\neq 0.$ The eight dimensional irreps reduce to four dimensional ones only when $λ$ and an eigenvalue of Hamiltonian satisfy a particular relation. The reduced four dimensional irreps are used to define $\mathbb{Z}_2^2$-graded supersymmetry transformations and two types of classical actions invariant under the transformations are presented. It is shown that one of the Noether charges vanishes if all the variables of specific $\mathbb{Z}_2^2$-degree are auxiliary.
