Non-linear Schroedinger Equations, Separation and Symmetry

Details Non-linear Schroedinger Equations, Separation and Symmetry Non-linear Schroedinger Equations, Separation and Symmetry

1999-06-29

arxiv.org/abs/quant-ph/9906117v1

J.Nonlin.Math.Phys. 2 (1995) 2-26

Physics

Quantum Physics

LaTeX, 31 pages

Scientific paper

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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