Resumo
Z2 × Z2-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 Z2 × Z2-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 Z2 × Z2-graded superalgebra are constructed for both
single multiplets and interacting multiplets. Furthermore, scale-invariant actions can possess
a full Z2 ×Z2-graded conformal invariance spanned by 10 generators and containing an sl(2)
subalgebra.