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Эта публикация цитируется в 7 научных статьях (всего в 7 статьях)
$\mathbb{Z}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics
Shunya Doi, Naruhiko Aizawa Department of Physical Science, Osaka Prefecture University, Nakamozu Campus, Sakai, Osaka 599-8531, Japan
Аннотация:
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.
Ключевые слова:
graded Lie superalgebras, superconformal mechanics.
Поступила: 24 марта 2021 г.; в окончательном варианте 14 июля 2021 г.; опубликована 20 июля 2021 г.
Образец цитирования:
Shunya Doi, Naruhiko Aizawa, “$\mathbb{Z}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics”, SIGMA, 17 (2021), 071, 14 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1753 https://www.mathnet.ru/rus/sigma/v17/p71
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