Wave Function of Anyon Systems

Anyon wave equations and the noncommutative plane

The “Jackiw-Nair” non-relativistic limit of the relativistic anyon equations provides us with infinite-component wave equations of the Dirac-Majorana-Lévy-Leblond type for the “exotic” particle, associated with the two-fold central extension of the planar Galilei group. An infinite dimensional representation of the Galilei group is found. The velocity operator is studied, and the observable coo...

Comment on "Partition function of anyon gas"

Laughlin Type Wave Function for Two–Dimensional Anyon Fields in a KMS–State

The correlation functions of two-dimensional anyon fields in a KMS-state are studied. The n-particle wave functions of noncanonical fermions of level ν, ν odd, are shown to be of Laughlin type of order ν. For the first noncanonical Fermi class (ν=3) this is simply the finite-temperature generalization of Laughlin wave function. This relates the first and second quantized pictures of the fractio...

Investigations of pairing in anyon systems.

We investigate pairing instabilities in the Fermi-liquid-like state of a single species of anyons. We describe the anyons as Fermions interacting with a Chern-Simons gauge field and consider the weak coupling limit where their statistics approaches that of Fermions. We show that, within the conventional BCS approach, due to induced repulsive Coulomb and current-current interactions, the attract...

On the origin of multi-component anyon wave functions

In this paper I discuss how the component structure of anyon wave functions arises in theories with non-relativistic matter coupled to a Chern-Simons gauge field on the torus. It is shown that there exists a singular gauge transformation which brings the Hamiltonian to free form. The gauge transformation removes a degree of freedom from the Hamiltonian. This degree of freedom generates only a f...