Nota de FísicaPublicado
The octonionically-induced exceptional superconformal quantum mechanics
Dados da publicação
- Autores
- —
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 12/12/2019
- Descrição
- Both the ${\cal N}=7$ superconformal quantum mechanics possessing the exceptional $G(3)$ Lie superalgebra as dynamical symmetry and its associated deformed oscillator with $G(3)$ as spectrum-generating superalgebra are presented.\par This superconformal quantum mechanics, uniquely defined up to similarity transformations, is obtained via the octonionically-induced ``quasi-nonassociative" method employed to derive the exceptional ${\cal N}=8$ $F(4)$ model. \par To construct the $G(3)$ theories, the covariant embedding of the $7$-dimensional representation of the Lie algebra $g_2$ within the $8\times 8$ matrices spanning the $Cl(0,7)$ Clifford algebra is derived.\par The Hilbert space of the $G(3)$ deformed oscillator is given by a $16$-ple of square-integrable functions of a real space coordinate. The spectrum of the theory is computed.
- Ano
- 2019
- Número
- CBPF-NF-005/19
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não