论文标题
$ {\ mathbb z} _2 \ times {\ mathbb z} _2 $ - 多颗粒量子量子哈密顿量
${\mathbb Z}_2\times {\mathbb Z}_2$-graded parastatistics in multiparticle quantum Hamiltonians
论文作者
论文摘要
$ {\ Mathbb Z} _2 \ times {\ Mathbb Z} _2 $不变的机制的最新兴趣激增构成了理解$ {\ Mathbb Z} _2 _2 \ times {\ MathB z} _2 _2 _2 $ Graded somementedmetermememmeterry的物理后果的挑战。在本文中表明，可以在理论的多片扇区中检测到非平凡的物理，这是由$ {\ mathbb z} _2 \ times {\ mathbb z} _2 _2 $ graded parastatistics诱发的。 $ {\ cal n} = 4 $ supersymmetric/ $ {\ mathbb z} _2 \ times {\ mathbb z} _2 $ graded振荡器的玩具模型。在此设置中，对于超对称性和$ {\ Mathbb Z} _2 \ times {\ Mathbb Z} _2 $ graded版本，一个粒子能级及其退化是相同的。然而，在多粒子扇区中，在合适状态下可观察到的操作员的测量可以区分所考虑的系统是否由普通玻色子/费米子组成，还是由$ {\ Mathbb Z} _2 _2 \ times {\ Mathbb Z} _2 _2 _2 $ graded graded粒子粒子组成。因此，$ {\ mathbb z} _2 \ times {\ mathbb z} _2 $ graded Mechanics具有实验测试的后果。此外，$ {\ mathbb z} _2 \ times {\ mathbb z} _2 $ - 级别限制可观察到的物品以遵守超选择规则。作为技术工具，将多片扇区编码在带有编织张量张量产品的分级谎言超级级别的超级代数的HOPF代数的相互作用中。
The recent surge of interest in ${\mathbb Z}_2\times {\mathbb Z}_2$-graded invariant mechanics poses the challenge of understanding the physical consequences of a ${\mathbb Z}_2\times{\mathbb Z}_2$-graded symmetry. In this paper it is shown that non-trivial physics can be detected in the multiparticle sector of a theory, being induced by the ${\mathbb Z}_2\times{\mathbb Z}_2$-graded parastatistics obeyed by the particles. The toy model of the ${\cal N}=4$ supersymmetric/ ${\mathbb Z}_2\times {\mathbb Z}_2$-graded oscillator is used. In this set-up the one-particle energy levels and their degenerations are the same for both supersymmetric and ${\mathbb Z}_2\times{\mathbb Z}_2$-graded versions. Nevertheless, in the multiparticle sector, a measurement of an observable operator on suitable states can discriminate whether the system under consideration is composed by ordinary bosons/fermions or by ${\mathbb Z}_2\times {\mathbb Z}_2$-graded particles. Therefore, ${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics has experimentally testable consequences. Furthermore, the ${\mathbb Z}_2\times {\mathbb Z}_2$-grading constrains the observables to obey a superselection rule. As a technical tool, the multiparticle sector is encoded in the coproduct of a Hopf algebra defined on a Universal Enveloping Algebra of a graded Lie superalgebra with a braided tensor product.
