On the relation between the anyon and Calogero models

V. I. Inozemtsev, Ryu Sasaki B

B. Basu-Mallick

Serguei B. Isakov, Jon Magne Leinaas

Farrokh Atai

This thesis deals with a conformal field theoretical treatment of abelian anyons in (1 + 1)-dimensions and their relation to the integrable Calogero-Sutherland models. We generalize previous work relating anyons to the Calogero-Sutherland model by showing that the correlation function of the anyon field operators corresponds to the eigenfunctions of the deformed Calogero-Sutherland model. Our results suggest a physical application of the deformed Calogero-Sutherland model in the context of the fractional quantum Hall effect (FQHE). A key aspect for this work is the introduction of the dual anyon field operators, which obey a natural generalization of the canonical anti-commutation relation.

Nico Kirchner, Frank Pollmann, Technische Universität München

Edwin Langmann A

We present remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers N and M, and a particular function of N+M variables arising as anyon correlation function of N particles and M antiparticles. In addition to identities obtained from anyons with the same statistics parameter λ, we also obtain “dual” relations involving “mixed” correlation functions of anyons with two different statistics parameters λ and 1∕λ. We also give alternative, elementary proofs of these identities by direct computations.