Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255695 | Journal of Geometry and Physics | 2018 | 11 Pages |
Abstract
We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic-geometric structure of this kind is observed in the context of pseudo-bosonic operators. Indeed we do not find the well known Heisenberg algebras, which are involved in several quantum dynamical systems, but different Lie algebras which may be decomposed into the sum of two abelian Lie algebras in a prescribed way. We introduce the notion of semidirect sum (of Lie algebras) for this scope and find that it describes very well the behavior of pseudo-bosonic operators in many quantum models.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Fabio Bagarello, Francesco G. Russo,