dorsal/arxiv
View SchemaOn the use of the group SO(4,2) in atomic and molecular physics
| Authors | Maurice Robert Kibler |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409209 |
| URL | https://arxiv.org/abs/quant-ph/0409209 |
| DOI | 10.1080/00268970410001728690 |
| Journal | Molecular Physics 102 (2004) 1221 |
Abstract
In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little groups. The second approach is by a new symmetry descent process starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional harmonic oscillator. It is based on the little known concept of a Lie algebra under constraints and corresponds in some sense to a symmetry breaking mechanism. This paper ends with a brief discussion of the interest of SO(4,2) for a new group-theoretical approach to the periodic table of chemical elements. In this connection, a general ongoing programme based on the use of a complete set of commuting operators is briefly described. It is believed that the present paper could be useful not only to the atomic and molecular community but also to people working in theoretical and mathematical physics.
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"abstract": "In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like\natom is derived through two different approaches. The first one is by an\nestablished traditional ascent process starting from the symmetry group SO(3).\nThis approach is presented in a mathematically oriented original way with a\nspecial emphasis on maximally superintegrable systems, N-dimensional extension\nand little groups. The second approach is by a new symmetry descent process\nstarting from the noninvariance dynamical group Sp(8,R) for a four-dimensional\nharmonic oscillator. It is based on the little known concept of a Lie algebra\nunder constraints and corresponds in some sense to a symmetry breaking\nmechanism. This paper ends with a brief discussion of the interest of SO(4,2)\nfor a new group-theoretical approach to the periodic table of chemical\nelements. In this connection, a general ongoing programme based on the use of a\ncomplete set of commuting operators is briefly described. It is believed that\nthe present paper could be useful not only to the atomic and molecular\ncommunity but also to people working in theoretical and mathematical physics.",
"arxiv_id": "quant-ph/0409209",
"authors": [
"Maurice Robert Kibler"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP",
"physics.atom-ph"
],
"doi": "10.1080/00268970410001728690",
"journal_ref": "Molecular Physics 102 (2004) 1221",
"title": "On the use of the group SO(4,2) in atomic and molecular physics",
"url": "https://arxiv.org/abs/quant-ph/0409209"
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