dorsal/arxiv
View SchemaAlgebraic nonlinear collective motion
| Authors | J. Troupe, G. Rosensteel |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9909071 |
| URL | https://arxiv.org/abs/nucl-th/9909071 |
| DOI | 10.1006/aphy.1998.5858 |
| Journal | Annals Phys. 270 (1998) 126-154 |
Abstract
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real number $\Lambda$. The $\Lambda=0$ solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positive $\Lambda$, the droplets have a neck that becomes more pronounced as $\Lambda$ increases; for negative $\Lambda$, the droplets contain a spherical bubble of radius $|\Lambda|^{{1/3}}$. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes ($\Lambda>0$) and bubble and two-fluid nuclei ($\Lambda<0$).
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"abstract": "Finite-dimensional Lie algebras of vector fields determine geometrical\ncollective models in quantum and classical physics. Every set of vector fields\non Euclidean space that generates the Lie algebra sl(3, R) and contains the\nangular momentum algebra so(3) is determined. The subset of divergence-free\nsl(3, R) vector fields is proven to be indexed by a real number $\\Lambda$. The\n$\\Lambda=0$ solution is the linear representation that corresponds to the\nRiemann ellipsoidal model. The nonlinear group action on Euclidean space\ntransforms a certain family of deformed droplets among themselves. For positive\n$\\Lambda$, the droplets have a neck that becomes more pronounced as $\\Lambda$\nincreases; for negative $\\Lambda$, the droplets contain a spherical bubble of\nradius $|\\Lambda|^{{1/3}}$. The nonlinear vector field algebra is extended to\nthe nonlinear general collective motion algebra gcm(3) which includes the\ninertia tensor. The quantum algebraic models of nonlinear nuclear collective\nmotion are given by irreducible unitary representations of the nonlinear gcm(3)\nLie algebra. These representations model fissioning isotopes ($\\Lambda\u003e0$) and\nbubble and two-fluid nuclei ($\\Lambda\u003c0$).",
"arxiv_id": "nucl-th/9909071",
"authors": [
"J. Troupe",
"G. Rosensteel"
],
"categories": [
"nucl-th"
],
"doi": "10.1006/aphy.1998.5858",
"journal_ref": "Annals Phys. 270 (1998) 126-154",
"title": "Algebraic nonlinear collective motion",
"url": "https://arxiv.org/abs/nucl-th/9909071"
},
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