
TL;DR
This paper classifies all quadratic algebras generated by creation and destruction operators with number operators, including bosons, fermions, and their generalizations, under certain symmetry and confluence conditions.
Contribution
It provides a complete enumeration of such algebras and introduces pseudo-bosons and pseudo-fermions as new generalizations.
Findings
Identifies all algebras of this type under given hypotheses
Shows these include known particles and their generalizations
Recovers q-bosons through algebra completion
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Advanced Topics in Algebra
