Journal of Nonlinear Mathematical Physics

Volume 2, Issue 1, February 1995, Pages 2 - 26

Non-linear Schrödinger Equations, Separation and Symmetry

Authors
George SVETLICHNY
Corresponding Author
George SVETLICHNY
Available Online 19 December 2006.
DOI
https://doi.org/10.2991/jnmp.1995.2.1.1How to use a DOI?
Abstract
We investigate the symmetry properties of hierarchies of non-linear Schrödinger equations, introduced in [2], 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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
2 - 1
Pages
2 - 26
Publication Date
2006/12
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.1995.2.1.1How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - George SVETLICHNY
PY  - 2006
DA  - 2006/12
TI  - Non-linear Schrödinger Equations, Separation and Symmetry
JO  - Journal of Nonlinear Mathematical Physics
SP  - 2
EP  - 26
VL  - 2
IS  - 1
SN  - 1402-9251
UR  - https://doi.org/10.2991/jnmp.1995.2.1.1
DO  - https://doi.org/10.2991/jnmp.1995.2.1.1
ID  - SVETLICHNY2006
ER  -