@article{Aizawa2024, 
author = {Naruhiko Aizawa and Ren Ito and Toshiya Tanaka},
title = {N    =  2 double graded supersymmetric quantum mechanics via dimensional reduction},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {5},
pages = {10494-10510},
keywords = {Z22-supersymmetry, constrained system, Dirac-Bergmann method, quantization, quantum mechanics},
url = {https://www.sciopen.com/article/10.3934/math.2024513},
doi = {10.3934/math.2024513},
abstract = {We presented a novel        N    =  2              Z        2    2  -graded supersymmetric quantum mechanics (                     Z            2      2      -SQM) which has different features from those introduced so far. It is a two-dimensional (two-particle) system and was the first example of the quantum mechanical realization of an eight-dimensional irreducible representation (irrep) of the        N    =  2              Z        2    2  -supersymmetry algebra. The                      Z            2      2      -SQM was obtained by quantizing the one-dimensional classical system derived by dimensional reduction from the two-dimensional                      Z            2      2      -supersymmetric Lagrangian of        N    =  1, which we constructed in our previous work. The ground states of the                      Z            2      2      -SQM were also investigated.}
}