| Autor: |
Doi, Shunya, Aizawa, Naruhiko |
| Rok vydání: |
2021 |
| Předmět: |
|
| Zdroj: |
SIGMA 17 (2021), 071, 14 pages |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.3842/SIGMA.2021.071 |
| Popis: |
Quantum mechanical systems whose symmetry is given by $\mathbb{Z}_2^3$-graded version of superconformal algebra are introduced. This is done by finding a realization of a $\mathbb{Z}_2^3$-graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. The realization allows us to map many models of superconformal quantum mechanics (SCQM) to their $\mathbb{Z}_2^3$-graded extensions. It is observed that for the simplest SCQM with $\mathfrak{osp}(1|2)$ symmetry there exist two inequivalent $\mathbb{Z}_2^3$-graded extensions. Applying the standard prescription of conformal quantum mechanics, spectrum of the SCQMs with the $\mathbb{Z}_2^3$-graded $\mathfrak{osp}(1|2)$ symmetry is analyzed. It is shown that many models of SCQM can be extended to $\mathbb{Z}_2^n$-graded setting. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
