A description of pseudo-bosons in terms of nilpotent Lie algebras

Fabio Bagarello, Francesco G. Russo, Fabio Bagarello

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.
Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalJournal of Geometry and Physics
Volume125
Publication statusPublished - 2018

Fingerprint

Nilpotent Lie Algebra
Bosons
Lie Algebra
algebra
bosons
Operator
Heisenberg Algebra
operators
Dynamical system
ladders
dynamical systems
Model

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Cite this

A description of pseudo-bosons in terms of nilpotent Lie algebras. / Bagarello, Fabio; Russo, Francesco G.; Bagarello, Fabio.

In: Journal of Geometry and Physics, Vol. 125, 2018, p. 1-11.

Research output: Contribution to journalArticle

Bagarello, Fabio ; Russo, Francesco G. ; Bagarello, Fabio. / A description of pseudo-bosons in terms of nilpotent Lie algebras. In: Journal of Geometry and Physics. 2018 ; Vol. 125. pp. 1-11.
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