|
| related topics |
| {operator, operators, space} |
| {field, particle, equation} |
| {let, theorem, proof} |
| {group, space, representation} |
| {equation, function, exp} |
| {particle, mechanics, theory} |
| {observables, space, algebra} |
|
Non-linear Schroedinger Equations, Separation and Symmetry
George Svetlichny
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.
- oai_identifier:
- oai:arXiv.org:quant-ph/9906117
- categories:
- quant-ph
- comments:
- LaTeX, 31 pages
- arxiv_id:
- quant-ph/9906117
- journal_ref:
- J.Nonlin.Math.Phys. 2 (1995) 2-26
- created:
- 1999-06-29
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