Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians

Abstract The recent surge of interest in Z 2 × -graded invariant mechanics poses the challenge understanding physical consequences a symmetry. In this paper it is shown that non-trivial physics can be detected multiparticle sector theory, being induced by parastatistics obeyed particles. toy model $\mathcal{N}=4$?> mathvariant="script">N = 4 supersymmetric/ oscillator used. set-up one-particle energy levels and their degenerations are same for both supersymmetric versions. Nevertheless, sector, measurement an observable operator on suitable states discriminate whether system under consideration composed ordinary bosons/fermions or Therefore, has experimentally testable consequences. Furthermore, -grading constrains observables to obey superselection rule. As technical tool, encoded coproduct Hopf algebra defined Universal enveloping graded Lie superalgebra with braided tensor product.