Non-linear Schrödinger Equations, Separation and Symmetry

DOI

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.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Download article (PDF)

TY  - JOUR
AU  - George Svetlichny
PY  - 1995
DA  - 1995/02/01
TI  - Non-linear Schrödinger Equations, Separation and Symmetry
JO  - Journal of Nonlinear Mathematical Physics
SP  - 2
EP  - 26
VL  - 2
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1995.2.1.1
DO  - 10.2991/jnmp.1995.2.1.1
ID  - Svetlichny1995
ER  -