Abstract
Abstract
The recent surge of interest in
Z
2
×
Z
2
-graded invariant mechanics poses the challenge of understanding the physical consequences of a
Z
2
×
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
Z
2
×
Z
2
-graded parastatistics obeyed by the particles. The toy model of the
N
=
4
supersymmetric/
Z
2
×
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
Z
2
×
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
Z
2
×
Z
2
-graded particles. Therefore,
Z
2
×
Z
2
-graded mechanics has experimentally testable consequences. Furthermore, the
Z
2
×
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.
Funder
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics
Cited by
21 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献