dorsal/arxiv
View SchemaNon-linear Schroedinger Equations, Separation and Symmetry
| Authors | George Svetlichny |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9906117 |
| URL | https://arxiv.org/abs/quant-ph/9906117 |
| Journal | J.Nonlin.Math.Phys. 2 (1995) 2-26 |
Abstract
We investigate the symmetry properties of hierarchies of non-linear Schroedinger equations (introduced by Doebner and Goldin, and Goldin and Svetlichny), which describe non-interacting systems in which tensor product wave-functions evolve by independent evolution of the factors (the separation property). We show that there are obstructions to lifting symmetries existing at a certain number of particles to higher numbers. Such obstructions vanish for particles without internal degrees of freedom and the usual space-time symmetries. For particles with internal degrees of freedom, such as spin, these obstructions are present and their circumvention requires a choice of a new term in the equation for each particle number. A Lie-algebra approach for non-linear theories is developed.
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"abstract": "We investigate the symmetry properties of hierarchies of non-linear\nSchroedinger equations (introduced by Doebner and Goldin, and Goldin and\nSvetlichny), which describe non-interacting systems in which tensor product\nwave-functions evolve by independent evolution of the factors (the separation\nproperty). We show that there are obstructions to lifting symmetries existing\nat a certain number of particles to higher numbers. Such obstructions vanish\nfor particles without internal degrees of freedom and the usual space-time\nsymmetries. For particles with internal degrees of freedom, such as spin, these\nobstructions are present and their circumvention requires a choice of a new\nterm in the equation for each particle number. A Lie-algebra approach for\nnon-linear theories is developed.",
"arxiv_id": "quant-ph/9906117",
"authors": [
"George Svetlichny"
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"journal_ref": "J.Nonlin.Math.Phys. 2 (1995) 2-26",
"title": "Non-linear Schroedinger Equations, Separation and Symmetry",
"url": "https://arxiv.org/abs/quant-ph/9906117"
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