ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics
Quantum mechanical systems whose symmetry is given by the ℤ³₂-graded version of superconformal algebra are introduced. This is done by finding a realization of a ℤ³₂-graded Lie superalgebra in terms of a standard Lie superalgebra and the Clifford algebra. The realization allows us to map many models...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2021
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211352 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | ℤ³₂-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics. Shunya Doi and Naruhiko Aizawa. SIGMA 17 (2021), 071, 14 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Quantum mechanical systems whose symmetry is given by the ℤ³₂-graded version of superconformal algebra are introduced. This is done by finding a realization of a ℤ³₂-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 ℤ³₂-graded extensions. It is observed that for the simplest SCQM with (1|2) symmetry, there exist two inequivalent ℤ³₂-graded extensions. Applying the standard prescription of conformal quantum mechanics, the spectrum of the SCQMs with the ℤ³₂-graded (1|2) symmetry is analyzed. It is shown that many models of SCQM can be extended to a ℤⁿ₂-graded setting.
|
|---|---|
| ISSN: | 1815-0659 |