2020/05/31 by N. Aizawa, Z. Kuznetsova, F. Toppan
Mathematics · Physics and Astronomy · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1016/j.nuclphysb.2021.115426
published as Nucl. Phys. B 967 (2021) 115426 · 30 pages. Final version to appear in Nucl. Phys. B
arxiv created 2021/04/27 · arxiv updated 2021/05/03
In the previous paper arXiv:2003.06470 we introduced the notion of \mathbb Z2×\mathbb Z2-graded classical mechanics and presented a general framework to construct, in the Lagrangian setting, the worldline sigma models invariant under a \mathbb Z2×\mathbb 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 \mathbb Z2×\mathbb 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 \mathbb Z2×\mathbb 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 \mathbb Z2×\mathbb Z2-graded symmetries possessed by the quantum Hamiltonians is given.