Number Operator Algebras
Mathematical Physics
2007-05-23 v1 math.MP
Quantum Algebra
Abstract
Under some hypotheses (symmetry, confluence), we enumerate all quadratically presented algebras, generated by creation and destruction operators, in which number operators exist. We show that these are algebras of bosons, fermions, their immediate generalizations that we call pseudo-bosons and pseudo-fermions, and also matrix algebras, in the finitely generated case. We then recover q-bosons (and pseudo-q-bosons) by a completion operation.
Cite
@article{arxiv.math-ph/0103017,
title = {Number Operator Algebras},
author = {Fabien Besnard},
journal= {arXiv preprint arXiv:math-ph/0103017},
year = {2007}
}
Comments
58 pages, no figure