Volume 2, Issue 1, February 1995, Pages 2 - 26
Non-linear Schrödinger Equations, Separation and Symmetry
Received 23 September 1994, Available Online 1 February 1995.
- 10.2991/jnmp.19126.96.36.199How to use a DOI?
We investigate the symmetry properties of hierarchies of non-linear Schrödinger equations, introduced in , 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.
- © 2006, the Authors. Published by Atlantis Press.
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Cite this article
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.19188.8.131.52 DO - 10.2991/jnmp.19184.108.40.206 ID - Svetlichny1995 ER -