--- title: "A three-dimensional superconformal quantum mechanics with sl(2|1) dynamical symmetry • CBPF Index" description: "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." canonical_url: "https://index.cbpf.br/es/publicacoes/6ad2a767639f62b11adbd022" locale: es meta: "og:description": "CBPF INDEX es el sistema de seguimiento de la producción científica y tecnológica del CBPF. En él se puede obtener la lista de publicaciones de artículos, libros, informes técnicos, etc. de toda la comunidad del CBPF." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QSB0aHJlZS1kaW1lbnNpb25hbCBzdXBlcmNvbmZvcm1hbCBxdWFudHVtIG1lY2hhbmljcyB3aXRoIHNsKDJ8MSkgZHluYW1pY2FsIHN5bW1ldHJ5%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_Ivan%2BE.%2BCunha%2Cdetalhe_~MjEvMDgvMjAxOQ%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmQwMjIi%2Cs_07N-mkzALvI3PAtx.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "A three-dimensional superconformal quantum mechanics with sl(2|1) dynamical symmetry • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_~QSB0aHJlZS1kaW1lbnNpb25hbCBzdXBlcmNvbmZvcm1hbCBxdWFudHVtIG1lY2hhbmljcyB3aXRoIHNsKDJ8MSkgZHluYW1pY2FsIHN5bW1ldHJ5%2Ctipo_~Tm90YSBkZSBGw61zaWNh%2Ccor_~I2E4MmMwMA%2Cautores_Ivan%2BE.%2BCunha%2Cdetalhe_~MjEvMDgvMjAxOQ%2Csecao_Publicaciones%2Cp_Ii9lcy9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmQwMjIi%2Cs_07N-mkzALvI3PAtx.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Nota de Física****Publicado** # **A three-dimensional superconformal quantum mechanics with **sl(2∣1)sl(2|1)sl(2∣1)** dynamical symmetry** **Ivan E. Cunha** 21/08/2019 [**Descargar PDF **1 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbd022/pdf) [**Contactar al responsable**]() ## **Datos de la publicación**
Autores
Ivan E. Cunha
Tipo
Nota de Física
Estado
Publicado
Fecha de publicación
21/08/2019
Descripción
We construct a three-dimensional superconformal quantum mechanics (and its associated de Alfaro-Fubini-Furlan deformed oscillator) possessing an $sl(2|1)$ dynamical symmetry. At a coupling parameter $\beta\neq 0$ the Hamiltonian contains a $\frac{1}{r^2}$ potential and a spin-orbit (hence, a first-order differential operator) interacting term. At $\beta=0$ four copies of undeformed three-dimensional oscillators are recovered. The Hamiltonian gets diagonalized in each sector of total $j$ and orbital $l$ angular momentum (the spin of the system is $\frac{1}{2}$). The Hilbert space of the deformed oscillator is given by a direct sum of $sl(2|1)$ lowest weight representations. The selection of the admissible Hilbert spaces at given values of the coupling constant $\beta$ is discussed. The spectrum of the model is computed. The vacuum energy (as a function of $\beta$) consists of a recursive zigzag pattern. The degeneracy of the energy eigenvalues grows linearly up to $E\sim \beta$ (in proper units) and quadratically for $E>\beta$. The orthonormal energy eigenstates are expressed in terms of the associated Laguerre polynomials and the spin spherical harmonics. The dimensional reduction of the model to $d=2$ produces two copies (for $\beta$ and $-\beta$, respectively) of the two-dimensional $sl(2|1)$ deformed oscillator. The dimensional reduction to $d=1$ produces the one-dimensional $D(2,1;\alpha)$ deformed oscillator, with $\alpha$ determined by $\beta$.
Año
2019
Número
CBPF-NF-002/19
Vínculo con tesis
No
Vínculo con beca
No
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