Anyons, Deformed Oscillator Algebras and Projectors

Details Anyons, Deformed Oscillator Algebras and Projectors Anyons, Deformed Oscillator Algebras and Projectors

2008-09-18

arxiv.org/abs/0809.3226v2

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, 3 figures; v2: minor clarifications, references added, published in Nuclear Physics B

Scientific paper

We initiate an algebraic approach to the many-anyon problem based on deformed oscillator algebras. The formalism utilizes a generalization of the deformed Heisenberg algebras underlying the operator solution of the Calogero problem. We define a many-body Hamiltonian and an angular momentum operator which are relevant for a linearized analysis in the statistical parameter nu. There exists a unique ground state and, in spite of the presence of defect lines, the anyonic weight lattices are completely connected by the application of the oscillators of the algebra. This is achieved by supplementing the oscillator algebra with a certain projector algebra.

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