Z2×Z2-graded mechanics: The quantization

In a previous paper we introduced the notion of Z2×Z2-graded classical mechanics and presented a general framework to construct, in the Lagrangian setting, the worldline sigma models invariant under a Z2×Z2-graded superalgebra. In this work we discuss at first the classical Hamiltonian formulation for a class of these models and later present their canonical quantization.