Resumo
The recent surge of interest in Z2 ˆ Z2-graded invariant mechanics poses the challenge of
understanding the physical consequences of a Z2 ˆ Z2-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 Z2 ˆ Z2-graded parastatistics obeyed by the particles.
The toy model of the N “ 4 supersymmetric/ Z2 ˆ Z2-graded oscillator is used. In
this set-up the one-particle energy levels and their degenerations are the same for both
supersymmetric and Z2 ˆ Z2-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 Z2 ˆ Z2-graded
particles. Therefore, Z2 ˆX Z2-graded mechanics has experimentally testable consequences.
Furthermore, the Z2 X Z2-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.