Resumo
In the previous paper arXiv:2003.06470 we introduced the notion of Z2 ˆZ2-graded classical mechanics and presented a general framework to construct, in the Lagrangian setting,
the worldline sigma models invariant under a Z2 ˆ Z2-graded superalgebra. In this work
we discuss at first the classical Hamiltonian formulation of some of these models and later
present their canonical quantization.
As the simplest application of the construction we recover the Z2 ˆ Z2-graded quantum
Hamiltonian introduced by Bruce and Duplij in arXiv:1904.06975. We prove that this is
the first example of a large class of Z2 ˆ Z2-graded quantum models. We derive in particular interacting multiparticle quantum Hamiltonians given by Hermitian, matrix, differential
operators. The interacting terms appear as non-diagonal entries in the matrices.
The construction of the Noether charges, both classical and quantum, is presented. A
comprehensive discussion of the different Z2 ˆ Z2-graded symmetries possessed by the quantum Hamiltonians is give