Loop groups, anyons and the Calogero-Sutherland model

Details Loop groups, anyons and the Calogero-Sutherland model Loop groups, anyons and the Calogero-Sutherland model

1998-05-12

arxiv.org/abs/math-ph/9805010v1

Commun.Math.Phys.201:1-34,1999

Physics

Mathematical Physics

34 pages, Latex

Scientific paper

10.1007/s002200050547

The positive energy representations of the loop group of U(1) are used to construct a boson-anyon correspondence. We compute all the correlation functions of our anyon fields and study an anyonic W-algebra of unbounded operators with a common dense domain. This algebra contains an operator with peculiar exchange relations with the anyon fields. This operator can be interpreted as a second quantised Calogero-Sutherland (CS) Hamiltonian and may be used to solve the CS model. In particular, we inductively construct all eigenfunctions of the CS model from anyon correlation functions, for all particle numbers and positive couplings.

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