论文标题
美元
${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics: the classical theory
论文作者
论文摘要
$ {\ mathbb z} _2 \ times {\ mathbb z} _2 $ graded机制允许四种类型的粒子：普通玻色子，两类的费米子（属于不同类别的费米子相互通勤）和外来玻色子。在本文中，我们构造了基本$ {\ Mathbb z} _2 \ times {\ Mathbb Z} _2 $ - 加入的世界线多重组（扩展了一维超对称的情况），并根据一般方案，是一般的计划，其不变的经典动作和不变的经典动作和全球sigma模型。这四个基本多重载有两个玻色子和两个费米子。 They are $(2,2,0)$, with two propagating bosons and two propagating fermions, $(1,2,1)_{[00]}$ (the ordinary boson is propagating, while the exotic boson is an auxiliary field), $(1,2,1)_{[11]}$ (the converse case, the exotic boson is propagating, while the ordinary boson is an辅助字段），最后是$（0,2,2）$，带有两个玻色辅辅助场。 $ {\ Mathbb z} _2 \ times {\ Mathbb z} _2 $ graded Superalgebra下的经典动作不变。此外，比例不变的动作可以具有完整的$ {\ Mathbb Z} _2 \ times {\ Mathbb Z} _2 $ - 级的保形不变性，由$ 10 $发电机跨越，并包含$ SL（2）$ subergebra。
${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics admits four types of particles: ordinary bosons, two classes of fermions (fermions belonging to different classes commute among each other) and exotic bosons. In this paper we construct the basic ${\mathbb Z}_2\times {\mathbb Z}_2$-graded worldline multiplets (extending the cases of one-dimensional supersymmetry) and compute, based on a general scheme, their invariant classical actions and worldline sigma-models. The four basic multiplets contain two bosons and two fermions. They are $(2,2,0)$, with two propagating bosons and two propagating fermions, $(1,2,1)_{[00]}$ (the ordinary boson is propagating, while the exotic boson is an auxiliary field), $(1,2,1)_{[11]}$ (the converse case, the exotic boson is propagating, while the ordinary boson is an auxiliary field) and, finally, $(0,2,2)$ with two bosonic auxiliary fields. Classical actions invariant under the ${\mathbb Z}_2\times {\mathbb Z}_2$-graded superalgebra are constructed for both single multiplets and interacting multiplets. Furthermore, scale-invariant actions can possess a full ${\mathbb Z}_2\times {\mathbb Z}_2$-graded conformal invariance spanned by $10$ generators and containing an $sl(2)$ subalgebra.
