Number Operator Algebras

Details Number Operator Algebras Number Operator Algebras

2001-03-13

arxiv.org/abs/math-ph/0103017v1

Physics

Mathematical Physics

58 pages, no figure

Scientific paper

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.

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